Journal articles: 'Least-Square estimator'

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Kwon, Bokyu, and Soohee Han. "Least-Mean-Square Receding Horizon Estimation." Mathematical Problems in Engineering 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/631759.

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We propose a least-mean-square (LMS) receding horizon (RH) estimator for state estimation. The proposed LMS RH estimator is obtained from the conditional expectation of the estimated state given a finite number of inputs and outputs over the recent finite horizon. Anya prioristate information is not required, and existing artificial constraints for easy derivation are not imposed. For a general stochastic discrete-time state space model with both system and measurement noise, the LMS RH estimator is explicitly represented in a closed form. For numerical reliability, the iterative form is presented with forward and backward computations. It is shown through a numerical example that the proposed LMS RH estimator has better robust performance than conventional Kalman estimators when uncertainties exist.

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Zulkifli, Raudhah, Nazim Aimran, Sayang Mohd Deni, and Fatin Najihah Badarisam. "A comparative study on the performance of maximum likelihood, generalized least square, scale-free least square, partial least square and consistent partial least square estimators in structural equation modeling." International Journal of Data and Network Science 6, no. 2 (2022): 391–400. http://dx.doi.org/10.5267/j.ijdns.2021.12.015.

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Structural equation modeling offers various estimation methods for estimating parameters. The most used method in covariance-based structural equation modeling (CB-SEM) is the maximum likelihood (ML) estimator. The ML estimator is typically used when fitting models with normally distributed data. The growth of partial least squares path modeling (PLS-PM), including consistent partial least squares (PLSc), has also been noticed by researchers in the SEM fields. The PLSc has elevated interest in the scholastic setting in measuring the performance of various estimation methods in structural equation modeling. The choice of estimation methods has substantial impact in yielding parameter estimates. There could be a trade-off among the estimation methods’ ability to deal with different types of data based on the model tested. Accordingly, this study aims to compare the performance of ML, generalized least squares (GLS), and scale-free least squares (SFLS) for CB-SEM as well as partial least squares (PLS) and consistent partial least squares (PLSc). Multivariate normal data were generated using Monte Carlo simulation with pre-determined population parameters and sample sizes using R Programming packages. To produce the estimated values, data analysis was performed using AMOS and SmartPLS for CB-SEM and PLS-SEM, respectively. The findings illustrate notable similarities between CB-SEM (ML) and PLS-SEM results when the true indicator loading is certainly high.

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Setiawan, Ezra Putranda, and Dedi Rosadi. "APPLICATION OF ROBUST REGRESSION FOR PORTFOLIO OPTIMIZATION." Matrix Science Mathematic 7, no. 1 (January 5, 2023): 07–15. http://dx.doi.org/10.26480/msmk.01.2023.07.15.

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The single-index model is a portfolio optimization method that uses each asset’s beta’. In general, the beta is estimated using the return data by the least square method. However, the return data frequently contains several outliers, so the estimation resulting from the least square method is inaccurate. This study examines several beta estimators from robust regression methods, namely the least absolute value estimator, M-estimator, LMS-estimator, LTS-estimator, MM-estimator, and Tau estimator to estimate the beta of each asset and make an optimal portfolio based on this estimated value. We also evaluate the effect of robust beta estimators on the stability and performance of each portfolio. We present the Sharpe ratio and some turnover measures, namely the l-period portfolio turnover, maximum turnover, lower bound single-asset turnover, and lower bound multiple-asset turnover. Among various estimators used here, the Tau estimator is the best estimator to replace the OLS for estimating the beta.

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Abdi, Hamdan, Sajaratud Dur, Rina Widyasar, and Ismail Husein. "Analysis of Efficiency of Least Trimmed Square and Least Median Square Methods in The Estimation of Robust Regression Parameters." ZERO: Jurnal Sains, Matematika dan Terapan 4, no. 1 (August 16, 2020): 21. http://dx.doi.org/10.30829/zero.v4i1.7933.

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<span lang="EN">Robust regression is a regression method used when the remainder's distribution is not reasonable, or there is an outreach to observational data that affects the model. One method for estimating regression parameters is the Least Squares Method (MKT). The method is easily affected by the presence of outliers. Therefore we need an alternative method that is robust to the presence of outliers, namely robust regression. Methods for estimating robust regression parameters include Least Trimmed Square (LTS) and Least Median Square (LMS). These methods are estimators with high breakdown points for outlier observational data and have more efficient algorithms than other estimation methods. This study aims to compare the regression models formed from the LTS and LMS methods, determine the efficiency of the model formed, and determine the factors that influence the production of community oil palm in Langkat District in 2018. The results showed that in testing, the estimated model of the regression parameters showed the same results. Compared to the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018</span>

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SÖKÜT AÇAR, Tuğba. "Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation." Journal of New Theory, no. 41 (December 31, 2022): 1–17. http://dx.doi.org/10.53570/jnt.1139885.

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The sensitivity of the least-squares estimation in a regression model is impacted by multicollinearity and autocorrelation problems. To deal with the multicollinearity, Ridge, Liu, and Ridge-type biased estimators have been presented in the statistical literature. The recently proposed Kibria-Lukman estimator is one of the Ridge-type estimators. The literature has compared the Kibria-Lukman estimator with the others using the mean square error criterion for the linear regression model. It was achieved in a study conducted on the Kibria-Lukman estimator's performance under the first-order autoregressive erroneous autocorrelation. When there is an autocorrelation problem with the second-order, evaluating the performance of the Kibria-Lukman estimator according to the mean square error criterion makes this paper original. The scalar mean square error of the Kibria-Lukman estimator under the second-order autoregressive error structure was evaluated using a Monte Carlo simulation and two real examples, and compared with the Generalized Least-squares, Ridge, and Liu estimators. The findings revealed that when the variance of the model was small, the mean square error of the Kibria-Lukman estimator gave very close values with the popular biased estimators. As the model variance grew, Kibria-Lukman did not give fairly similar values with popular biased estimators as in the model with small variance. However, according to the mean square error criterion the Kibria-Lukman estimator outperformed the Generalized Least-Squares estimator in all possible cases.

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Mohmadishak Sheikh, Chetan Sheth. "System State Estimation Using Weighted Least Square Method." Proceeding International Conference on Science and Engineering 11, no. 1 (February 18, 2023): 1294–99. http://dx.doi.org/10.52783/cienceng.v11i1.276.

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State estimation is an essential part of every energy control management system. Accurate estimation of state or operating state is essential for security control and monitoring of power systems. Power system state estimation is a procedure to estimate true state from the inexact state of a power system. The conventional state estimator provides estimates of the power system states, i.e., bus voltages and angles which is obtained. State estimation is a computational technique for electrical power system. It empowers the calculation of the power flows of the electrical power system which are not observed or not directly measured. State estimation is a computer program that detects, isolate and eliminate the incorrect or bad measurement data and estimates the accurate state. The magnitudes of bus voltage and phase angle are the states variables for an electrical power system. This paper outlines Weighted Least Square (WLS) estimation techniques and simulated estimation for standard IEEE systems.

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Chetan Sheth, Mohmadishak Sheikh,. "Power System State Estimation using Weighted Least Square Method." Proceeding International Conference on Science and Engineering 11, no. 1 (February 18, 2023): 1721–27. http://dx.doi.org/10.52783/cienceng.v11i1.327.

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State estimation is an essential part of every energy control management system. Accurate estimation of state or operating state is essential for security control and monitoring of power systems. Power system state estimation is a procedure to estimate true state from the inexact state of a power system. The conventional state estimator provides estimates of the power system states, i.e., bus voltages and angles which is obtained. State estimation is a computational technique for electrical power system. It empowers the calculation of the power flows of the electrical power system which are not observed or not directly measured. State estimation is a computer program that detects, isolate and eliminate the incorrect or bad measurement data and estimates the accurate state. The magnitudes of bus voltage and phase angle are the states variables for an electrical power system. This paper outlines Weighted Least Square (WLS) estimation techniques and simulated estimation for standard IEEE systems.

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Aladeitan, BENEDICTA, Adewale F. Lukman, Esther Davids, Ebele H. Oranye, and Golam B. M. Kibria. "Unbiased K-L estimator for the linear regression model." F1000Research 10 (August 19, 2021): 832. http://dx.doi.org/10.12688/f1000research.54990.1.

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Background: In the linear regression model, the ordinary least square (OLS) estimator performance drops when multicollinearity is present. According to the Gauss-Markov theorem, the estimator remains unbiased when there is multicollinearity, but the variance of its regression estimates become inflated. Estimators such as the ridge regression estimator and the K-L estimators were adopted as substitutes to the OLS estimator to overcome the problem of multicollinearity in the linear regression model. However, the estimators are biased, though they possess a smaller mean squared error when compared to the OLS estimator. Methods: In this study, we developed a new unbiased estimator using the K-L estimator and compared its performance with some existing estimators theoretically, simulation wise and by adopting real-life data. Results: Theoretically, the estimator even though unbiased also possesses a minimum variance when compared with other estimators. Results from simulation and real-life study showed that the new estimator produced smaller mean square error (MSE) and had the smallest mean square prediction error (MSPE). This further strengthened the findings of the theoretical comparison using both the MSE and the MSPE as criterion. Conclusions: By simulation and using a real-life application that focuses on modelling, the high heating values of proximate analysis was conducted to support the theoretical findings. This new method of estimation is recommended for parameter estimation with and without multicollinearity in a linear regression model.

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Adedia, David, Atinuke O. Adebanji, and Simon Kojo Appiah. "Comparative Analysis of Some Structural Equation Model Estimation Methods with Application to Coronary Heart Disease Risk." Journal of Probability and Statistics 2020 (September 22, 2020): 1–15. http://dx.doi.org/10.1155/2020/4181426.

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This study compared a ridge maximum likelihood estimator to Yuan and Chan (2008) ridge maximum likelihood, maximum likelihood, unweighted least squares, generalized least squares, and asymptotic distribution-free estimators in fitting six models that show relationships in some noncommunicable diseases. Uncontrolled hypertension has been shown to be a leading cause of coronary heart disease, kidney dysfunction, and other negative health outcomes. It poses equal danger when asymptomatic and undetected. Research has also shown that it tends to coexist with diabetes mellitus (DM), with the presence of DM doubling the risk of hypertension. The study assessed the effect of obesity, type II diabetes, and hypertension on coronary risk and also the existence of converse relationship with structural equation modelling (SEM). The results showed that the two ridge estimators did better than other estimators. Nonconvergence occurred for most of the models for asymptotic distribution-free estimator and unweighted least squares estimator whilst generalized least squares estimator had one nonconvergence of results. Other estimators provided competing outputs, but unweighted least squares estimator reported unreliable parameter estimates such as large chi-square test statistic and root mean square error of approximation for Model 3. The maximum likelihood family of estimators did better than others like asymptotic distribution-free estimator in terms of overall model fit and parameter estimation. Also, the study found that increase in obesity could result in a significant increase in both hypertension and coronary risk. Diastolic blood pressure and diabetes have significant converse effects on each other. This implies those who are hypertensive can develop diabetes and vice versa.

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Dey, Sanku, Mahendra Saha, and Sankar Goswami. "One Parameter A (α) Distribution: Different Methods of Estimation." Spectrum: Science and Technology 8, no. 1 (December 15, 2021): 01–09. http://dx.doi.org/10.54290/spect/2021.v8.1.0001.

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This paper addresses the different methods of estimation of the unknown parameter of one parameter A(α) distribution from the frequentist point of view. We briefly describe different approaches, namely, maximum likelihood estimator, least square and weighted least square estimators, maximum product spacing estimators, Cram´er-von Mises estimator and compare those using extensive numerical simulations. Next, we obtain parametric bootstrap confidence interval of the parameter using frequentist approaches. Finally, one real data set has been analysed for illustrative purposes.

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Yang, Yaoting, Weizhong Tian, and Tingting Tong. "Generalized Mixtures of Exponential Distribution and Associated Inference." Mathematics 9, no. 12 (June 13, 2021): 1371. http://dx.doi.org/10.3390/math9121371.

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A new generalization of the exponential distribution, namely the generalized mixture of exponential distribution, is introduced. Some of its basic properties, such as hazard function, moments, order statistics, mean deviation, measures of uncertainly, and reliability probability, are studied. Three different estimation methods are investigated by the maximum likelihood estimator, least-square estimator, and weighted least-square estimator. The performances of the estimators are assessed by simulation studies. Real-world applications of the proposed distribution are explored, and data fitting results show that the new distribution performs better than its competitors.

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Messer, H., and Y. Bar-Ness. "Closed-loop least mean square time-delay estimator." IEEE Transactions on Acoustics, Speech, and Signal Processing 35, no. 4 (April 1987): 413–24. http://dx.doi.org/10.1109/tassp.1987.1165163.

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Kalina, Jan, and Jan Tichavský. "On Robust Estimation of Error Variance in (Highly) Robust Regression." Measurement Science Review 20, no. 1 (February 1, 2020): 6–14. http://dx.doi.org/10.2478/msr-2020-0002.

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AbstractThe linear regression model requires robust estimation of parameters, if the measured data are contaminated by outlying measurements (outliers). While a number of robust estimators (i.e. resistant to outliers) have been proposed, this paper is focused on estimating the variance of the random regression errors. We particularly focus on the least weighted squares estimator, for which we review its properties and propose new weighting schemes together with corresponding estimates for the variance of disturbances. An illustrative example revealing the idea of the estimator to down-weight individual measurements is presented. Further, two numerical simulations presented here allow to compare various estimators. They verify the theoretical results for the least weighted squares to be meaningful. MM-estimators turn out to yield the best results in the simulations in terms of both accuracy and precision. The least weighted squares (with suitable weights) remain only slightly behind in terms of the mean square error and are able to outperform the much more popular least trimmed squares estimator, especially for smaller sample sizes.

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Ibrahim, Nur Farahiah, Zahari Abu Bakar, and Azlina Idris. "Improving Space-Time-Frequency MIMO-OFDM with ICI Self-Cancellation Scheme using Least Square Error Estimator." Scientific Research Journal 12, no. 1 (June 1, 2015): 25. http://dx.doi.org/10.24191/srj.v12i1.5436.

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Channel estimation techniques for Multiple-input Multiple-output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) based on comb type pilot arrangement with least-square error (LSE) estimator was investigated with space-time-frequency (STF) diversity implementation. The frequency offset in OFDM effected its performance. This was mitigated with the implementation of the presented inter-carrier interference self-cancellation (ICI-SC) techniques and different space-time subcarrier mapping. STF block coding in the system exploits the spatial, temporal and frequency diversity to improve performance. Estimated channel was fed into a decoder which combined the STF decoding together with the estimated channel coefficients using LSE estimator for equalization. The performance of the system was compared by measuring the symbol error rate with a PSK-16 and PSK-32. The results show that subcarrier mapping together with ICI-SC were able to increase the system performance. Introduction of channel estimation was also able to estimate the channel coefficient at only 5dB difference with a perfectly known channel.

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Rahmawati, Dyah P., I. N. Budiantara, Dedy D. Prastyo, and Made A. D. Octavanny. "Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression." International Journal of Mathematics and Mathematical Sciences 2021 (March 11, 2021): 1–14. http://dx.doi.org/10.1155/2021/6611084.

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Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.

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Satyanarayana and B. Ismail. "GENERALISED LEAST SQUARE RATIO ESTIMATOR IN HETEROSCEDASTIC REGRESSION MODEL." Advances and Applications in Statistics 86, no. 2 (April 11, 2023): 207–27. http://dx.doi.org/10.17654/0972361723023.

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Alhaj, H. M. M., N. M. Nor, Vijanth S. Asirvadam, M. F. Abdullah, and T. Ibrahim. "Estimation of Power System Harmonic Using Modified Normalized Least Mean Square." Applied Mechanics and Materials 785 (August 2015): 378–82. http://dx.doi.org/10.4028/www.scientific.net/amm.785.378.

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A new adaptive power system harmonic estimator is presented, which is competent of tracking power system harmonic components. The proposed estimator technique is based on the normalized Least Mean Square (LMS), which is a stochastic gradient descent algorithm. The learning method of the proposed estimator is based upon the recursive estimate of the signal power, and is faster tracking of harmonic components as compared to the introduced Adaptive Linear Element (ADALINE).

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Et al., Khaleel. "Estimating the Reliability Function of (2+1) Cascade Model." Baghdad Science Journal 16, no. 2 (June 2, 2019): 0395. http://dx.doi.org/10.21123/bsj.16.2.0395.

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This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

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Et al., Khaleel. "Estimating the Reliability Function of (2+1) Cascade Model." Baghdad Science Journal 16, no. 2 (June 2, 2019): 0395. http://dx.doi.org/10.21123/bsj.2019.16.2.0395.

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This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

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Basetti, Vedik, and Ashwani Kumar Chandel. "Power system static state estimation using a least winsorized square robust estimator." Neurocomputing 207 (September 2016): 457–68. http://dx.doi.org/10.1016/j.neucom.2016.05.023.

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Robin, Jean-Marc, and Richard J. Smith. "TESTS OF RANK." Econometric Theory 16, no. 2 (April 2000): 151–75. http://dx.doi.org/10.1017/s0266466600162012.

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This paper considers tests for the rank of a matrix for which a root-T consistent estimator is available. However, in contrast to tests associated with the minimum chi-square and asymptotic least squares principles, the estimator's asymptotic variance matrix is not required to be either full or of known rank. Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables. These weights may be simply estimated, yielding convenient estimators for the limiting distributions of the proposed statistics. A sequential testing procedure is presented that yields a consistent estimator for the rank of a matrix. A simulation experiment is conducted comparing the characteristic root statistics advocated in this paper with statistics based on the Wald and asymptotic least squares principles.

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Badawaire, Abdulrasheed Bello, Kayode Ayinde, and S. O. Olanrewaju. "Addressing Autocorrelation, Multicollinearity, and Heavy-Tail Errors in the Linear Regression Model." Asian Journal of Probability and Statistics 26, no. 9 (August 28, 2024): 61–83. http://dx.doi.org/10.9734/ajpas/2024/v26i9646.

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The most popular estimator for estimating parameters of linear regression models is the Ordinary Least Squares (OLS) Estimator. The OLS is considered the best linear unbiased estimator when certain assumptions are not violated. However, when autocorrelation, multicollinearity, and heavy-tail error are jointly present in the dataset, the OLS estimator is inefficient and imprecise. In this paper, we developed an estimator of linear regression model parameters that jointly handle multicollinearity, autocorrelation, and heavy tail errors. The new estimator, LADHLKL, was derived by combining the Hildreth-Lu (HL), the Kibria Lukman (KL), and the Least Absolute Deviation (LAD) estimators. The LADHLKL poses both the characteristics of the LAD, HL, and KL estimators which makes it resistant to both problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and simulation study revealed that the proposed estimator dominates other estimators in all the considered conditions in terms of mean square error.

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IDOWU, Janet Iyabo, Olasunkanmi James OLADAPO, Abiola Timothy OWOLABİ, Kayode AYİNDE, and Oyinlade AKİNMOJU. "Combating Multicollinearity: A New Two-Parameter Approach." Nicel Bilimler Dergisi 5, no. 1 (June 30, 2023): 1–31. http://dx.doi.org/10.51541/nicel.1084768.

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The ordinary least square (OLS) estimator is the Best Linear Unbiased Estimator (BLUE) when all linear regression model assumptions are valid. The OLS estimator, however, becomes inefficient in the presence of multicollinearity. To circumvent the problem of multicollinearity, various one and two-parameter estimators have been proposed. This paper a new two-parameter estimator called Liu-Kibria Lukman Estimator (LKL) estimator. The theoretical and simulation results show that the proposed estimator performs better than some existing estimators considered in this study under some conditions, using the mean square error criterion. A real-life application to Portland cement and Longley datasets supported the theoretical and simulation results.

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Al-Omari, Amer Ibrahim, SidAhmed Benchiha, and Ibrahim M. Almanjahie. "Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design." Mathematics 10, no. 17 (September 2, 2022): 3170. http://dx.doi.org/10.3390/math10173170.

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An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study.

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Budiantara, I. Nyoman. "APLIKASI SPLINE ESTIMATOR TERBOBOT." Jurnal Teknik Industri 3, no. 2 (July 2, 2004): 57–62. http://dx.doi.org/10.9744/jti.3.2.57-62.

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We considered the nonparametric regression model : Zj = X(tj) + ej, j = 1,2, ,n, where X(tj) is the regression curve. The random error ej are independently distributed normal with a zero mean and a variance s2/bj, bj > 0. The estimation of X obtained by minimizing a Weighted Least Square. The solution of this optimation is a Weighted Spline Polynomial. Further, we give an application of weigted spline estimator in nonparametric regression. Abstract in Bahasa Indonesia : Diberikan model regresi nonparametrik : Zj = X(tj) + ej, j = 1,2, ,n, dengan X (tj) kurva regresi dan ej sesatan random yang diasumsikan berdistribusi normal dengan mean nol dan variansi s2/bj, bj > 0. Estimasi kurva regresi X yang meminimumkan suatu Penalized Least Square Terbobot, merupakan estimator Polinomial Spline Natural Terbobot. Selanjutnya diberikan suatu aplikasi estimator spline terbobot dalam regresi nonparametrik. Kata kunci: Spline terbobot, Regresi nonparametrik, Penalized Least Square.

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Espinosa, Sebastian, Jorge F. Silva, Rene A. Mendez, Rodrigo Lobos, and Marcos Orchard. "Optimality of the maximum likelihood estimator in astrometry." Astronomy & Astrophysics 616 (August 2018): A95. http://dx.doi.org/10.1051/0004-6361/201732537.

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Context. Astrometry relies on the precise measurement of the positions and motions of celestial objects. Driven by the ever-increasing accuracy of astrometric measurements, it is important to critically assess the maximum precision that could be achieved with these observations. Aims. The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramér–Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on a charge-coupled device (CCD)-like detector using commonly adopted estimators such as the weighted least squares and the maximum likelihood. Methods. Novel technical results are presented to determine the performance of an estimator that corresponds to the solution of an optimization problem in the context of astrometry. Using these results we are able to place stringent bounds on the bias and the variance of the estimators in close form as a function of the data. We confirm these results through comparisons to numerical simulations under a broad range of realistic observing conditions. Results. The maximum likelihood and the weighted least square estimators are analyzed. We confirm the sub-optimality of the weighted least squares scheme from medium to high signal-to-noise found in an earlier study for the (unweighted) least squares method. We find that the maximum likelihood estimator achieves optimal performance limits across a wide range of relevant observational conditions. Furthermore, from our results, we provide concrete insights for adopting an adaptive weighted least square estimator that can be regarded as a computationally efficient alternative to the optimal maximum likelihood solution. Conclusions. We provide, for the first time, close-form analytical expressions that bound the bias and the variance of the weighted least square and maximum likelihood implicit estimators for astrometry using a Poisson-driven detector. These expressions can be used to formally assess the precision attainable by these estimators in comparison with the minimum variance bound.

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Zhao, Wenzhi, Yinqian Yang, and Di Zhang. "A Two-Stage Estimator for Change Point in the Mean of Panel Data." Journal of Mathematics 2021 (September 17, 2021): 1–6. http://dx.doi.org/10.1155/2021/1455812.

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In this paper, a two-stage consistency estimator for change point in the mean of panel data is given. Firstly, a single sequence is extracted, and the initial estimator and confidence interval of the change point are given by the least square method. Based on the confidence interval, a random interval containing change point with probability tending to 1 is constructed. Secondly, using all panel data falling into the random interval, the final estimator of change point is obtained by least square estimation. The asymptotic distribution is established. Simulation results show that our method can not only ensure the estimation accuracy but also greatly reduce time complexity.

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Khalaf, Ghadban. "A Proposed Ridge Parameter to Improve the Least Square Estimator." Journal of Modern Applied Statistical Methods 11, no. 2 (November 1, 2012): 443–49. http://dx.doi.org/10.22237/jmasm/1351743240.

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Jasem, Haneen A., and Nada S. Karam. "Stress – strength p(X<Y<Z) reliability of n-cascade system for the new Weibull-pareto distribution." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012060. http://dx.doi.org/10.1088/1742-6596/2322/1/012060.

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Abstract In this paper, is derived the reliability of an n-cascade stress-strength system based on the New Weibull-Pareto Distribution (NWPD) with known β and θ parameters, λ unknown λ parameter, for probability of n- components having X, Z two stresses between them strengths Y. In NWPD, there are four methods of parameters and this system reliability estimators (the Maximum Likelihood, Moments, Least Square and Weighted Least Square Methods) are discussed, based estimators on the simulation technique, these estimates are compared by criteria the mean square error were used to compare small, medium and large samples. It has been concluded that the greatest maximum likelihood estimator performs all of the other options considered.

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Abonazel, Mohamed. "Bias correction methods for dynamic panel data models with fixed effects." International Journal of Applied Mathematical Research 6, no. 2 (May 24, 2017): 58. http://dx.doi.org/10.14419/ijamr.v6i2.7774.

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This paper considers the estimation methods for dynamic panel data (DPD) models with fixed effects, which suggested in econometric literature, such as least squares (LS) and generalized method of moments (GMM). These methods obtain biased estimators for DPD models. The LS estimator is inconsistent when the time dimension (T) is short regardless of the cross-sectional dimension (N). Although consistent estimates can be obtained by GMM procedures, the inconsistent LS estimator has a relatively low variance and hence can lead to an estimator with lower root mean square error after the bias is removed. Therefore, we discuss in this paper the different methods to correct the bias of LS and GMM estimations. The analytical expressions for the asymptotic biases of the LS and GMM estimators have been presented for large N and finite T. Finally; we display new estimators that presented by Youssef and Abonazel [40] as more efficient estimators than the conventional estimators.

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GÜL, Hasan Hüseyin. "Unit-Weibull Distribution: Different Method of Estimations." Karadeniz Fen Bilimleri Dergisi 13, no. 2 (June 15, 2023): 547–60. http://dx.doi.org/10.31466/kfbd.1239446.

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Recently, the unit-Weibull (UW) distribution, which is used quite effectively in analyzing lifetime data. The main goal of this article is to investigate the performance of seven estimation methods namely, maximum likelihood (ML), least square (LS), weighted least square (WLS), Anderson-Darling (AD), right-tail Anderson-Darling (RAD), Cramer-von-Mises (CVM) and percentile (PCE) for parameter estimation. An extensive Monte Carlo simulation study is considered to compare the performances of these methods through biases and mean square errors (MSEs). The numerical results show that the PCE estimator is significantly more smallest MSE value for different sample sizes and parameter values in most cases. In addition, the ML and LS estimators have lower bias values than the other estimators in general. Finally, a real data set is presented for illustrative purposes.

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Abdullah, Muhammad, Tahir N. Malik, Ali Ahmed, Muhammad F. Nadeem, Irfan A. Khan, and Rui Bo. "A Novel Hybrid GWO-LS Estimator for Harmonic Estimation Problem in Time Varying Noisy Environment." Energies 14, no. 9 (May 1, 2021): 2587. http://dx.doi.org/10.3390/en14092587.

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The power quality of the Electrical Power System (EPS) is greatly affected by electrical harmonics. Hence, accurate and proper estimation of electrical harmonics is essential to design appropriate filters for mitigation of harmonics and their associated effects on the power quality of EPS. This paper presents a novel statistical (Least Square) and meta-heuristic (Grey wolf optimizer) based hybrid technique for accurate detection and estimation of electrical harmonics with minimum computational time. The non-linear part (phase and frequency) of harmonics is estimated using GWO, while the linear part (amplitude) is estimated using the LS method. Furthermore, harmonics having transients are also estimated using proposed harmonic estimators. The effectiveness of the proposed harmonic estimator is evaluated using various case studies. Comparing the proposed approach with other harmonic estimation techniques demonstrates that it has a minimum mean square error with less complexity and better computational efficiency.

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LI, R., F. LI, and J. W. HUANG. "THE PREDICTIVE PERFORMANCE EVALUATION AND NUMERICAL EXAMPLE STUDY FOR THE PRINCIPAL COMPONENT TWO-PARAMETERS ESTIMATOR." Latin American Applied Research - An international journal 48, no. 3 (October 8, 2019): 181–86. http://dx.doi.org/10.52292/j.laar.2018.223.

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In this paper, detailed comparisons are given between those estimators that can be derived from the principal component two-parameter estimator such as the ordinary least squares estimator, the principal components regression estimator, the ridge regression estimator, the Liu estimator, the r-k estimator and the r-d estimator by the prediction mean square error criterion. In addition, conditions for the superiority of the principal component two-parameter estimator over the others are obtained. Furthermore, a numerical example study is conducted to compare these estimators under the prediction mean squared error criterion.

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Mehta, Shubham, Harish Ramani, Nileshkumar N. Yelgatte, and Imran Rahman. "Recursive Orthogonal Least Square Based Soft Sensor for Batch Distillation." Chemical Product and Process Modeling 11, no. 3 (September 1, 2016): 241–63. http://dx.doi.org/10.1515/cppm-2015-0071.

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Abstract A multiple-input and multiple-output (MIMO) model, namely Recursive Orthogonal Least Square (ROLS) based radial basis function (RBF) is developed to estimate product compositions in a batch distillation process from temperature measurements. The process data is generated by simulating the differential equations of the batch distillation process, changing the initial feed composition and boiluprate from batch to batch. Moreover, the reflux ratio is also randomly varied within each batch to represent the exact dynamics of the batch distillation. Temperature and distillate composition is correlated by the RBF trained by ROLS algorithm. A Single RBF network estimate the quality of products in real-time. The results show that ROLS based estimator give correct composition estimations for a batch distillation process. The robustness of the ROLS algorithm and low computational requirement makes the estimator attractive for on-line use.

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Islamiyati, Anna, Anisa Anisa, Raupong Raupong, Jusmawati Massalesse, Nasrah Sirajang, Sitti Sahriman, and Alfiana Wahyuni. "Estimasi Model Regresi Spline Kubik Tersegmen dengan Metode Penalized Least Square." Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam 10, no. 2 (October 23, 2022): 139–48. http://dx.doi.org/10.24256/jpmipa.v10i2.3197.

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Abstract:Nonparametric regression is used for data whose data pattern is non-parametric. One of the estimators that can be developed is a segmented cubic spline which is able to show several segmentation changes in the data. This article examines the estimation of segmented cubic spline nonparametric regression models using the Penalized Least Square estimation criteria. The method involves knot points and smoothing parameters simultaneously. In addition, the model is used to analyze data on BPJS claims based on patient age. The results show that the optimal model is at two-knot points, namely 26 and 52 with a smoothing parameter of 0.89. There are three segmentation changes from the cubic data, which consist of young people up to 26 years old, 26-52 years old, and 52 years and over. Abstrak:Regresi nonparametrik digunakan untuk data yang pola datanya bentuk non parametrik. Salah satu estimator yang dapat dikembangkan adalah spline kubik tersegmen yang mampu menunjukkan beberapa segmentasi perubahan pada data. Artikel ini mengkaji estimasi model regresi nonparametrik spline kubik tersegmen melalui kriteria estimasi menggunakan Penalized Least Square. Metode tersebut melibatkan titik knot dan parameter penghalus secara bersamaan. Selain itu, model digunakan untuk menganalisis data klaim BPJS berdasarkan usia pasien. Hasil menunjukkan bahwa model optimal pada dua titik knot yaitu 26 dan 52 dengan parameter penghalus sebesar 0,89. Terdapat tiga segmentasi perubahan data secara kubik, yaitu usia muda hingga 26 tahun, usia 26-52 tahun, dan usia 52 tahun ke atas.

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Wang, Hai Jun, Yan Zhen, Qing Hai Ou, Hong Yu Zhang, Wan Qing Yang, and Yuan Dou Xia. "Comparison of Downlink Channel Estimation Schemes for LTE-Based Smart Grid Communications." Applied Mechanics and Materials 713-715 (January 2015): 962–65. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.962.

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The long term evolution (LTE) based smart grid communication network is a promising candidate solution for the future power grid. In this paper, we discuss three channel estimation schemes for the LTE-based smart grids, including least square (LS), minimum mean square error (MMSE), and discrete Fourier transform (DFT) based channel estimators. In the simulations, we compare these three estimators, the results show that the DFT-based channel estimator can achieve the best tradeoff between the performance and the implementation complexity.

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Yasmeen, Uzma, Muhammad Noor-ul-Amin, and Muhammad Hanif. "Variance estimation in stratified adaptive cluster sampling." Statistics in Transition New Series 23, no. 1 (March 1, 2022): 173–84. http://dx.doi.org/10.2478/stattrans-2022-0010.

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Abstract In many sampling surveys, the use of auxiliary information at either the design or estimation stage, or at both these stages is usual practice. Auxiliary information is commonly used to obtain improved designs and to achieve a high level of precision in the estimation of population density. Adaptive cluster sampling (ACS) was proposed to observe rare units with the purpose of obtaining highly precise estimations of rare and specially clustered populations in terms of least variances of the estimators. This sampling design proved to be more precise than its more conventional counterparts, including simple random sampling (SRS), stratified sampling, etc. In this paper, a generalised estimator is anticipated for a finite population variance with the use of information of an auxiliary variable under stratified adaptive cluster sampling (SACS). The bias and mean square error expressions of the recommended estimators are derived up to the first degree of approximation. A simulation study showed that the proposed estimators have the least estimated mean square error under the SACS technique in comparison to variance estimators in stratified sampling.

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N. S. Karam and H. A. Jasem. "Gumbel Type -2 Stress – Strength P(X<Y<Z) n-Cascade Reliability Estimation." Mustansiriyah Journal of Pure and Applied Sciences 1, no. 2 (July 1, 2023): 86–100. http://dx.doi.org/10.47831/mjpas.v1i2.34.

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In this paper, is derived the reliability of n-cascade stress-strength system model based on the Gumbel Type- 2 Distribution (GT-2) with unknown parameter λ and known parameters β , for probability of n- components having strengths Y between two stresses X and Z .In the Gumbel Type- 2 Distribution ,there are six methods of parameters and this system reliability estimators where discussed by using the Maximum Likelihood, Moments Method, Least Square Method, Weighted Least Square Method , Regression and Percentile ,based estimators on the simulation technique , these estimates are compared by the mean square error criteria for both small, medium and large samples .It has been concluded that the maximum likelihood estimator performs better than all the options considered.

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Salarzadeh Jenatabadi, Hashem, Che Wan Jasimah Bt Wan Mohamed Radzi, and Nadia Samsudin. "Associations of Body Mass Index with Demographics, Lifestyle, Food Intake, and Mental Health among Postpartum Women: A Structural Equation Approach." International Journal of Environmental Research and Public Health 17, no. 14 (July 18, 2020): 5201. http://dx.doi.org/10.3390/ijerph17145201.

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As postpartum obesity is becoming a global public health challenge, there is a need to apply postpartum obesity modeling to determine the indicators of postpartum obesity using an appropriate statistical technique. This research comprised two phases, namely: (i) development of a previously created postpartum obesity modeling; (ii) construction of a statistical comparison model and introduction of a better estimator for the research framework. The research model displayed the associations and interactions between the variables that were analyzed using the Structural Equation Modeling (SEM) method to determine the body mass index (BMI) levels related to postpartum obesity. The most significant correlations obtained were between BMI and other substantial variables in the SEM analysis. The research framework included two categories of data related to postpartum women: living in urban and rural areas in Iran. The SEM output with the Bayesian estimator was 81.1%, with variations in the postpartum women’s BMI, which is related to their demographics, lifestyle, food intake, and mental health. Meanwhile, the variation based on SEM with partial least squares estimator was equal to 70.2%, and SEM with a maximum likelihood estimator was equal to 76.8%. On the other hand, the output of the root mean square error (RMSE), mean absolute error (MSE) and mean absolute percentage error (MPE) for the Bayesian estimator is lower than the maximum likelihood and partial least square estimators. Thus, the predicted values of the SEM with Bayesian estimator are closer to the observed value compared to maximum likelihood and partial least square. In conclusion, the higher values of R-square and lower values of MPE, RMSE, and MSE will produce better goodness of fit for SEM with Bayesian estimators.

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Ekiz, Meltem, and Osman Ufuk Ekiz. "Modelling Tap Water Consumer Ratio." Mathematics 8, no. 9 (September 10, 2020): 1557. http://dx.doi.org/10.3390/math8091557.

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Increasing population and the rising air temperatures are known as factors that cause water depletion in the watersheds. Therefore, it is important to accurately predict the future ratios of tap water consumers using the same watershed to the population living in the specified area, to produce better water policies and to take the necessary measures. Predictions can be made by a growth curve model (GCM). Parameter estimations of the GCM are usually based on the ordinary least square (OLS) estimator. However, the outlier presence affects the estimations and the predictions, which are obtained by using the estimated model. The present article attempts to construct first- and third-order GCMs with robust least median square (LMS) and M estimators to make short-term predictions of ratios of tap water consumers. According to the findings, parameter estimations of the models, the outliers, and the predictions vary with respect to the estimators. The M estimator for short-term predictions is suggested for use, due to its robustness against outlier points.

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R, Aditya Setyawan, Mustika Hadijati, and Ni Wayan Switrayni. "Analisis Masalah Heteroskedastisitas Menggunakan Generalized Least Square dalam Analisis Regresi." EIGEN MATHEMATICS JOURNAL 1, no. 2 (December 31, 2019): 61. http://dx.doi.org/10.29303/emj.v1i2.43.

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Regression analysis is one statistical method that allows users to analyze the influence of one or more independent variables (X) on a dependent variable (Y).The most commonly used method for estimating linear regression parameters is Ordinary Least Square (OLS). But in reality, there is often a problem with heteroscedasticity, namely the variance of the error is not constant or variable for all values of the independent variable X. This results in the OLS method being less effective. To overcome this, a parameter estimation method can be used by adding weight to each parameter, namely the Generalized Least Square (GLS) method. This study aims to examine the use of the GLS method in overcoming heteroscedasticity in regression analysis and examine the comparison of estimation results using the OLS method with the GLS method in the case of heteroscedasticity.The results show that the GLS method was able to maintain the nature of the estimator that is not biased and consistent and able to overcome the problem of heteroscedasticity, so that the GLS method is more effective than the OLS method.

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Octavanny, Made Ayu Dwi, I. Nyoman Budiantara, Heri Kuswanto, and Dyah Putri Rahmawati. "Nonparametric Regression Model for Longitudinal Data with Mixed Truncated Spline and Fourier Series." Abstract and Applied Analysis 2020 (December 9, 2020): 1–11. http://dx.doi.org/10.1155/2020/4710745.

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Existing literature in nonparametric regression has established a model that only applies one estimator to all predictors. This study is aimed at developing a mixed truncated spline and Fourier series model in nonparametric regression for longitudinal data. The mixed estimator is obtained by solving the two-stage estimation, consisting of a penalized weighted least square (PWLS) and weighted least square (WLS) optimization. To demonstrate the performance of the proposed method, simulation and real data are provided. The results of the simulated data and case study show a consistent finding.

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Saputri, Gustina, Netti Herawati, Tiryono Ruby, and Khoirin Nisa. "Comparative Study in Controlling Outliers and Multicollinearity Using Robust Performance Jackknife Ridge Regression Estimator Based on Generalized-M and Least Trimmed Square Estimator." Jambura Journal of Mathematics 6, no. 2 (August 1, 2024): 147–51. http://dx.doi.org/10.37905/jjom.v6i2.24828.

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Regression analysis is one of the statistical methods used to determine the causal relationship between one or more explanatory variables to the affected variable. The problem that often occurs in regression analysis is that there are multicollonity and outliers. To deal with such problems can be solved using ridge regression analysis and robust regression. Ridge regression can solve the problem of multicollinearas by assigning a constant k to the matrix Z′Z. But in this method the resulting bias value is still high, so to overcome this problem, the jackknife ridge regression method is used. Meanwhile, to overcome outliers in the data using robust regression methods which have several estimation methods, two of which are the Generalized-M (GM) estimator and the Least Trimmed Square (LTS) estimator. The aim of the study is to solve the problem of multicollinearity and outliers simultaneously using robust jackknife ridge regression method with GM estimators and LTS estimators. The results showed that the robust ridge jackknife regression method with LTS estimator can control multicollinearity and outliers simultaneously better based on MSE, AIC and BIC values compared to the robust ridge jackknife regression method with GM estimators. This is indicated by the value MSE = -6.60371, AIC = 75.823 and BIC = 81.642 on LTS estimators that are of lower value than GM estimators.

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Laksaci, Ali, Salim Bouzebda, Fatimah Alshahrani, Ouahiba Litimein, and Boubaker Mechab. "Spatio-Functional Local Linear Asymmetric Least Square Regression Estimation: Application for Spatial Prediction of COVID-19 Propagation." Symmetry 15, no. 12 (November 23, 2023): 2108. http://dx.doi.org/10.3390/sym15122108.

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The problem of estimating the spatio-functional expectile regression for a given spatial mixing structure Xi,Yi∈F×R, when i∈ZN,N≥1 and F is a metric space, is investigated. We have proposed the M-estimation procedure to construct the Spatial Local Linear (SLL) estimator of the expectile regression function. The main contribution of this study is the establishment of the asymptotic properties of the SLL expectile regression estimator. Precisely, we establish the almost-complete convergence with rate. This result is proven under some mild conditions on the model in the mixing framework. The implementation of the SLL estimator is evaluated using an empirical investigation. A COVID-19 data application is performed, allowing this work to highlight the substantial superiority of the SLL-expectile over SLL-quantile in risk exploration.

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Standsyah, Rahmawati Erma, Bambang Widjanarko Otok, and Agus Suharsono. "Fixed Effect Meta-Analytic Structural Equation Modeling (MASEM) Estimation Using Generalized Method of Moments (GMM)." Symmetry 13, no. 12 (November 29, 2021): 2273. http://dx.doi.org/10.3390/sym13122273.

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The fixed effect meta-analytic structural equation modeling (MASEM) model assumes that the population effect is homogeneous across studies. It was first developed analytically using Generalized Least Squares (GLS) and computationally using Weighted Least Square (WLS) methods. The MASEM fixed effect was not estimated analytically using the estimation method based on moment. One of the classic estimation methods based on moment is the Generalized Method of Moments (GMM), whereas GMM can possibly estimate the data whose studies has parameter uncertainty problems, it also has a high accuracy on data heterogeneity. Therefore, this study estimates the fixed effect MASEM model using GMM. The symmetry of this research is based on the proof goodness of the estimator and the performance that it is analytical and numerical. The estimation results were proven to be the goodness of the estimator, unbiased and consistent. To show the performance of the obtained estimator, a comparison was carried out on the same data as the MASEM using GLS. The results show that the estimation of MASEM using GMM yields the SE value in each coefficient is smaller than the estimation of MASEM using GLS. Interactive GMM for the determination of the optimal weight on GMM in this study gave better results and therefore needs to be developed in order to obtain a Random Model MASEM estimator using GMM that is much more reliable and accurate in performance.

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Ebrahem, Mohammed Al-Haj, and Mohammad Abedalqader. "Estimating percentiles of time-to-failure distribution obtained from a Weibull accelerated degradation model." Journal of Statistics and Management Systems 28, no. 1 (2025): 79–87. https://doi.org/10.47974/jsms-1207.

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We propose a nonparametric kernel estimation method to estimate the percentiles of the time-to-failure distribution under the usual use condition obtained from a Weibull accelerated degradation model. We discuss some of the well-known parametric method that used to estimate the time-to-failure distribution and its percentile under the usual use condition including ordinary least square method and maximum likelihood method. The different exiting methods were compared with the kernel method through simulation by using the mean square error and the bootstrap confidence interval length. In general, when the distributional assumption is available, the maximum likelihood estimator performs better than the other two estimators, while the kernel estimator performs better than the other two estimators when the distributional assumption is not available. Application to real data set was disscuced.

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Jenq, Yih-Chyun. "High-precision sinusoidal frequency estimator based on weighted least square method." IEEE Transactions on Instrumentation and Measurement IM-36, no. 1 (March 1987): 124–27. http://dx.doi.org/10.1109/tim.1987.6312644.

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Essai Ali, Mohamed Hassan, Ali R. Abdellah, Hany A. Atallah, Gehad Safwat Ahmed, Ammar Muthanna, and Andrey Koucheryavy. "Deep Learning Peephole LSTM Neural Network-Based Channel State Estimators for OFDM 5G and Beyond Networks." Mathematics 11, no. 15 (August 2, 2023): 3386. http://dx.doi.org/10.3390/math11153386.

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This study uses deep learning (DL) techniques for pilot-based channel estimation in orthogonal frequency division multiplexing (OFDM). Conventional channel estimators in pilot-symbol-aided OFDM systems suffer from performance degradation, especially in low signal-to-noise ratio (SNR) regions, due to noise amplification in the estimation process, intercarrier interference, a lack of primary channel data, and poor performance with few pilots, although they exhibit lower complexity and require implicit knowledge of the channel statistics. A new method for estimating channels using DL with peephole long short-term memory (peephole LSTM) is proposed. The proposed peephole LSTM-based channel state estimator is deployed online after offline training with generated datasets to track channel parameters, which enables robust recovery of transmitted data. A comparison is made between the proposed estimator and conventional LSTM and GRU-based channel state estimators using three different DL optimization techniques. Due to the outstanding learning and generalization properties of the DL-based peephole LSTM model, the suggested estimator significantly outperforms the conventional least square (LS) and minimum mean square error (MMSE) estimators, especially with a few pilots. The suggested estimator can be used without prior information on channel statistics. For this reason, it seems promising that the proposed estimator can be used to estimate the channel states of an OFDM communication system.

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Gorgees, Hazim Mansoor, and Fatimah Assim Mahdi. "The Comparison Between Different Approaches to Overcome the Multicollinearity Problem in Linear Regression Models." Ibn AL- Haitham Journal For Pure and Applied Science 31, no. 1 (May 14, 2018): 212. http://dx.doi.org/10.30526/31.1.1841.

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In the presence of multi-collinearity problem, the parameter estimation method based on the ordinary least squares procedure is unsatisfactory. In 1970, Hoerl and Kennard insert analternative method labeled as estimator of ridge regression. In such estimator, ridge parameter plays an important role in estimation. Various methods were proposed by many statisticians to select the biasing constant (ridge parameter). Another popular method that is used to deal with the multi-collinearity problem is the principal component method. In this paper,we employ the simulation technique to compare the performance of principal component estimator with some types of ordinary ridge regression estimators based on the value of the biasing constant (ridge parameter). The mean square error (MSE) is used as a criterion to assess the performance of such estimators.

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Ocran, By E., R. Minkah, and K. Doku-Amponsah. "A reduced-bias weighted least squares estimation of the extreme value index." Journal of Statistics and Management Systems 27, no. 8 (2024): 1499–523. https://doi.org/10.47974/jsms-981.

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In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed) distributions. This is derived using the weighted least squares method. It is shown that the estimator is asymptotically unbiased, asymptotically consistent and asymptotically normal under the second-order conditions on the underlying distribution of the data. The finite sample properties of the proposed estimator are studied through a simulation study. The results show that it is competitive to the existing estimators of the extreme value index in terms of bias and Mean Square Error. In addition, it yields estimates of g > 0 that are less sensitive to the number of top-order statistics, and hence, it alleviate the problem of selecting an optimal tail fraction to some extent. The proposed estimator is further illustrated using practical datasets from pedochemical and insurance.

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Journal articles on the topic 'Least-Square estimator'

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