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Journal articles on the topic 'Weighted regression estimator'

Author: Grafiati

Published: 8 September 2023

Last updated: 31 July 2025

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1

Kalina, Jan, and Jan Tichavský. "On Robust Estimation of Error Variance in (Highly) Robust Regression." Measurement Science Review 20, no. 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 i

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2

Zhou, Xiaoshuang, Xiulian Gao, Yukun Zhang, Xiuling Yin, and Yanfeng Shen. "Efficient Estimation for the Derivative of Nonparametric Function by Optimally Combining Quantile Information." Symmetry 13, no. 12 (2021): 2387. http://dx.doi.org/10.3390/sym13122387.

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In this article, we focus on the efficient estimators of the derivative of the nonparametric function in the nonparametric quantile regression model. We develop two ways of combining quantile regression information to derive the estimators. One is the weighted composite quantile regression estimator based on the quantile weighted loss function; the other is the weighted quantile average estimator based on the weighted average of quantile regression estimators at a single quantile. Furthermore, by minimizing the asymptotic variance, the optimal weight vector is computed, and consequently, the o

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3

Cai, Zongwu. "REGRESSION QUANTILES FOR TIME SERIES." Econometric Theory 18, no. 1 (2002): 169–92. http://dx.doi.org/10.1017/s0266466602181096.

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In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for α-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, v

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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 commonl

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Koenker, Roger, and Kevin F. Hallock. "Quantile Regression." Journal of Economic Perspectives 15, no. 4 (2001): 143–56. http://dx.doi.org/10.1257/jep.15.4.143.

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Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.

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Zhang, Zhengyu. "LOCAL PARTITIONED QUANTILE REGRESSION." Econometric Theory 33, no. 5 (2016): 1081–120. http://dx.doi.org/10.1017/s0266466616000293.

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In this paper, we consider the nonparametric estimation of a broad class of quantile regression models, in which the partially linear, additive, and varying coefficient models are nested. We propose for the model a two-stage kernel-weighted least squares estimator by generalizing the idea of local partitioned mean regression (Christopeit and Hoderlein, 2006, Econometrica 74, 787–817) to a quantile regression framework. The proposed estimator is shown to have desirable asymptotic properties under standard regularity conditions. The new estimator has three advantages relative to existing methods

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Zheng, Cheng, Sayan Dasgupta, Yuxiang Xie, Asad Haris, and Ying-Qing Chen. "On Data-Enriched Logistic Regression." Mathematics 13, no. 3 (2025): 441. https://doi.org/10.3390/math13030441.

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Biomedical researchers typically investigate the effects of specific exposures on disease risks within a well-defined population. The gold standard for such studies is to design a trial with an appropriately sampled cohort. However, due to the high cost of such trials, the collected sample sizes are often limited, making it difficult to accurately estimate the effects of certain exposures. In this paper, we discuss how to leverage the information from external ”big data” (datasets with significantly larger sample sizes) to improve the estimation accuracy at the risk of introducing a small amou

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Schreuder, H. T., H. G. Li, and J. W. Hazard. "PPS and Random Sampling Estimation Using some Regression and Ratio Estimators for Underlying Linear and Curvilinear Models." Forest Science 33, no. 4 (1987): 997–1009. http://dx.doi.org/10.1093/forestscience/33.4.997.

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Abstract Two thousand samples of 30 units were drawn from selected populations for which linear or curvilinear underlying models were postulated between the variable of interest and a covariate. Ratio, and linear and nonlinear regression estimators were compared for bias and relative efficiency of the estimates generated. Regression estimators were found to be the most precise estimators of totals for both random and probability proportional to size (PPS) sampling for a series of tree populations for samples of size 30. The weighted regression estimator in PPS sampling was consistently more ef

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Tao, Li, Lingnan Tai, Manling Qian, and Maozai Tian. "A New Instrumental-Type Estimator for Quantile Regression Models." Mathematics 11, no. 15 (2023): 3412. http://dx.doi.org/10.3390/math11153412.

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This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The weights assigned to each estimator are determined by the inverses of their corresponding individual variance–covariance matrices. The implementation of the estimation has many advantages in terms of computational efforts and simplifies the asymptotic distribution. Furthermore, the paper shows c

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Glynn, Adam N., and Kevin M. Quinn. "An Introduction to the Augmented Inverse Propensity Weighted Estimator." Political Analysis 18, no. 1 (2010): 36–56. http://dx.doi.org/10.1093/pan/mpp036.

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In this paper, we discuss an estimator for average treatment effects (ATEs) known as the augmented inverse propensity weighted (AIPW) estimator. This estimator has attractive theoretical properties and only requires practitioners to do two things they are already comfortable with: (1) specify a binary regression model for the propensity score, and (2) specify a regression model for the outcome variable. Perhaps the most interesting property of this estimator is its so-called “double robustness.” Put simply, the estimator remains consistent for the ATE if either the propensity score model or th

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Laome, Lilis, I. Nyoman Budiantara, and Vita Ratnasari. "Estimation Curve of Mixed Spline Truncated and Fourier Series Estimator for Geographically Weighted Nonparametric Regression." Mathematics 11, no. 1 (2022): 152. http://dx.doi.org/10.3390/math11010152.

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Geographically Weighted Regression (GWR) is the development of multiple linear regression models used in spatial data. The assumption of spatial heterogeneity results in each location having different characteristics and allows the relationships between the response variable and each predictor variable to be unknown, hence nonparametric regression becomes one of the alternatives that can be used. In addition, regression functions are not always the same between predictor variables. This study aims to use the Geographically Weighted Nonparametric Regression (GWNR) model with a mixed estimator o

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Schreuder, H. T., and Z. Ouyang. "Optimal sampling strategies for weighted linear regression estimation." Canadian Journal of Forest Research 22, no. 2 (1992): 239–47. http://dx.doi.org/10.1139/x92-031.

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Our strong effort to find an optimal sampling strategy that was clearly superior to other strategies for a range of linearity conditions and variance structures for linear models showed that several sampling strategies turned out to be equally efficient. Each of these stratified the population to the maximum extent feasible, i.e., used n strata based on a covariate. Which of two ways of stratification to use and how units in each stratum were selected (simple random sampling or sampling with probability proportional to size) did not seem to matter much. Two regression estimators, one consideri

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Shemail, Ayad H., and Mohammed J. Mohammed. "Semi Parametric Logistic Regression Model with the Outputs Representing Trapezoidal Intuitionistic Fuzzy Number." Journal of Economics and Administrative Sciences 28, no. 133 (2022): 70–81. http://dx.doi.org/10.33095/jeas.v28i133.2350.

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In this paper, the fuzzy logic and the trapezoidal fuzzy intuitionistic number were presented, as well as some properties of the trapezoidal fuzzy intuitionistic number and semi- parametric logistic regression model when using the trapezoidal fuzzy intuitionistic number. The output variable represents the dependent variable sometimes cannot be determined in only two cases (response, non-response)or (success, failure) and more than two responses, especially in medical studies; therefore so, use a semi parametric logistic regression model with the output variable (dependent variable) representin

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Luo, Shuanghua, Cheng-yi Zhang, and Meihua Wang. "Composite Quantile Regression for Varying Coefficient Models with Response Data Missing at Random." Symmetry 11, no. 9 (2019): 1065. http://dx.doi.org/10.3390/sym11091065.

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Composite quantile regression (CQR) estimation and inference are studied for varying coefficient models with response data missing at random. Three estimators including the weighted local linear CQR (WLLCQR) estimator, the nonparametric WLLCQR (NWLLCQR) estimator, and the imputed WLLCQR (IWLLCQR) estimator are proposed for unknown coefficient functions. Under some mild conditions, the proposed estimators are asymptotic normal. Simulation studies demonstrate that the unknown coefficient estimators with IWLLCQR are superior to the other two with WLLCQR and NWLLCQR. Moreover, bootstrap test proce

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Octavanny, Made Ayu Dwi, I. Nyoman Budiantara, Heri Kuswanto, and Dyah Putri Rahmawati. "A New Mixed Estimator in Nonparametric Regression for Longitudinal Data." Journal of Mathematics 2021 (November 15, 2021): 1–12. http://dx.doi.org/10.1155/2021/3909401.

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We introduce a new method for estimating the nonparametric regression curve for longitudinal data. This method combines two estimators: truncated spline and Fourier series. This estimation is completed by minimizing the penalized weighted least squares and weighted least squares. This paper also provides the properties of the new mixed estimator, which are biased and linear in the observations. The best model is selected using the smallest value of generalized cross-validation. The performance of the new method is demonstrated by a simulation study with a variety of time points. Then, the prop

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Kong, Efang, Oliver Linton, and Yingcun Xia. "GLOBAL BAHADUR REPRESENTATION FOR NONPARAMETRIC CENSORED REGRESSION QUANTILES AND ITS APPLICATIONS." Econometric Theory 29, no. 5 (2013): 941–68. http://dx.doi.org/10.1017/s0266466612000813.

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This paper is concerned with the nonparametric estimation of regression quantiles of a response variable that is randomly censored. Using results on the strong uniform convergence rate of U-processes, we derive a global Bahadur representation for a class of locally weighted polynomial estimators, which is sufficiently accurate for many further theoretical analyses including inference. Implications of our results are demonstrated through the study of the asymptotic properties of the average derivative estimator of the average gradient vector and the estimator of the component functions in censo

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17

Zhang, Yichong, and Xin Zheng. "Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization." Quantitative Economics 11, no. 3 (2020): 957–82. http://dx.doi.org/10.3982/qe1323.

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In this paper, we study the estimation and inference of the quantile treatment effect under covariate‐adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the in

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18

Bhat, S. S., and R. Vidya. "Performance of Ridge Estimators Based on Weighted Geometric Mean and Harmonic Mean." Journal of Scientific Research 12, no. 1 (2020): 1–13. http://dx.doi.org/10.3329/jsr.v12i1.40525.

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Ordinary least squares estimator (OLS) becomes unstable if there is a linear dependence between any two predictors. When such situation arises ridge estimator will yield more stable estimates to the regression coefficients than OLS estimator. Here we suggest two modified ridge estimators based on weights, where weights being the first two largest eigen values. We compare their MSE with some of the existing ridge estimators which are defined in the literature. Performance of the suggested estimators is evaluated empirically for a wide range of degree of multicollinearity. Simulation study indic

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Millar, Russell B. "A better estimator of mortality rate from age-frequency data." Canadian Journal of Fisheries and Aquatic Sciences 72, no. 3 (2015): 364–75. http://dx.doi.org/10.1139/cjfas-2014-0193.

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The Chapman–Robson and weighted-regression estimators are currently the two preferred methods for estimation of instantaneous mortality, z, from a cross-sectional sample of age-frequency data. They are derived under the assumption of steady-state population dynamics. Here, a new estimator is developed from a population model that explicitly includes annual variability in recruitment. The new estimator is trivial to implement using existing generalized linear mixed model software. It is vastly superior to both the Chapman–Robson and weighted-regression estimators under a wide range of simulatio

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Yang, Hojin, Hongtu Zhu, Mihye Ahn, and Joseph G. Ibrahim. "Weighted functional linear Cox regression model." Statistical Methods in Medical Research 30, no. 8 (2021): 1917–31. http://dx.doi.org/10.1177/09622802211012015.

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The aim of this paper is to develop a weighted functional linear Cox regression model that accounts for the association between a failure time and a set of functional and scalar covariates. We formulate the weighted functional linear Cox regression by incorporating a comprehensive three-stage estimation procedure as a unified methodology. Specifically, the weighted functional linear Cox regression uses a functional principal component analysis to represent the functional covariates and a high-dimensional Cox regression model to capture the joint effects of both scalar and functional covariates

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Nurcahayani, Helida, I. Nyoman Budiantara, and Ismaini Zain. "The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression." Mathematics 9, no. 10 (2021): 1141. http://dx.doi.org/10.3390/math9101141.

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Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objecti

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Lee, Kyuseok. "A weighted Fama-MacBeth two-step panel regression procedure: asymptotic properties, finite-sample adjustment, and performance." Studies in Economics and Finance 37, no. 2 (2020): 347–60. http://dx.doi.org/10.1108/sef-08-2019-0322.

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Purpose In a recent paper, Yoon and Lee (2019) (YL hereafter) propose a weighted Fama and MacBeth (FMB hereafter) two-step panel regression procedure and provide evidence that their weighted FMB procedure produces more efficient coefficient estimators than the usual unweighted FMB procedure. The purpose of this study is to supplement and improve their weighted FMB procedure, as they provide neither asymptotic results (i.e. consistency and asymptotic distribution) nor evidence on how close their standard error estimator is to the true standard error. Design/methodology/approach First, asymptoti

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23

Newey, Whitney K. "CONDITIONAL MOMENT RESTRICTIONS IN CENSORED AND TRUNCATED REGRESSION MODELS." Econometric Theory 17, no. 5 (2001): 863–88. http://dx.doi.org/10.1017/s0266466601175018.

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Censored and truncated regression models with unknown distribution are important in econometrics. This paper characterizes the class of all conditional moment restrictions that lead to √n-consistent estimators for these models. The semiparametric efficiency bound for each conditional moment restriction is derived. In the case of a nonzero bound it is shown how an estimator can be constructed and that an appropriately weighted version can attain the efficiency bound. These estimators also work when the disturbance is independent of the regressors. The paper discusses combining conditional momen

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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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De Luca, Giuseppe, and Jan R. Magnus. "Bayesian Model Averaging and Weighted-Average Least Squares: Equivariance, Stability, and Numerical Issues." Stata Journal: Promoting communications on statistics and Stata 11, no. 4 (2011): 518–44. http://dx.doi.org/10.1177/1536867x1201100402.

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In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by

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Oliveira, Thiago Wendling Gonçalves de, Rafael Rubilar, Carlos Roberto Sanquetta, Ana Paula Dalla Corte, and Alexandre Behling. "Simultaneous estimation as an alternative to young eucalyptus aboveground biomass modeling in ecophysiological experiments." Acta Scientiarum. Agronomy 43 (July 5, 2021): e52126. http://dx.doi.org/10.4025/actasciagron.v43i1.52126.

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Accurate forest biomass estimates require the selection of appropriate models of individual trees. Thus, two properties are required in tree biomass modeling: (1) additivity of biomass components and (2) estimator efficiency. This study aimed to develop a system of equations to estimate young eucalyptus aboveground biomass and guarantee additivity and estimator efficiency. Aboveground eucalyptus biomass models were calibrated using four methods: generalized least squares (GLS), weighted least squares (WLS), seemingly unrelated regression (SUR), and weighted seemingly unrelated regression (WSUR

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Chamidah, Nur, Budi Lestari, I. Nyoman Budiantara, and Dursun Aydin. "Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator." Symmetry 16, no. 4 (2024): 386. http://dx.doi.org/10.3390/sym16040386.

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In data analysis using a nonparametric regression approach, we are often faced with the problem of analyzing a set of data that has mixed patterns, namely, some of the data have a certain pattern and the rest of the data have a different pattern. To handle this kind of datum, we propose the use of a mixed estimator. In this study, we theoretically discuss a developed estimation method for a nonparametric regression model with two or more response variables and predictor variables, and there is a correlation between the response variables using a mixed estimator. The model is called the multire

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Fransiska, Welly, Sigit Nugroho, and Ramya Rachmawati. "A Comparison of Weighted Least Square and Quantile Regression for Solving Heteroscedasticity in Simple Linear Regression." Journal of Statistics and Data Science 1, no. 1 (2022): 19–29. http://dx.doi.org/10.33369/jsds.v1i1.21011.

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Regression analysis is the study of the relationship between dependent variable and one or more independent variables. One of the important assumption that must be fulfilled to get the regression coefficient estimator Best Linear Unbiased Estimator (BLUE) is homoscedasticity. If the homoscedasticity assumption is violated then it is called heteroscedasticity. The consequences of heteroscedasticity are the estimator remain linear and unbiased, but it can cause estimator haven‘t a minimum variance so the estimator is no longer BLUE. The purpose of this study is to analyze and resolve the violati

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Kalina, J., and J. Tichavský. "Statistical learning for recommending (robust) nonlinear regression methods." Journal of Applied Mathematics, Statistics and Informatics 15, no. 2 (2019): 47–59. http://dx.doi.org/10.2478/jamsi-2019-0008.

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Abstract We are interested in comparing the performance of various nonlinear estimators of parameters of the standard nonlinear regression model. While the standard nonlinear least squares estimator is vulnerable to the presence of outlying measurements in the data, there exist several robust alternatives. However, it is not clear which estimator should be used for a given dataset and this question remains extremely difficult (or perhaps infeasible) to be answered theoretically. Metalearning represents a computationally intensive methodology for optimal selection of algorithms (or methods) and

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Sriliana, Idhia, I. Nyoman Budiantara, and Vita Ratnasari. "A Truncated Spline and Local Linear Mixed Estimator in Nonparametric Regression for Longitudinal Data and Its Application." Symmetry 14, no. 12 (2022): 2687. http://dx.doi.org/10.3390/sym14122687.

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Longitudinal data modeling is widely carried out using parametric methods. However, when the parametric model is misspecified, the obtained estimator might be severely biased and lead to erroneous conclusions. In this study, we propose a new estimation method for longitudinal data modeling using a mixed estimator in nonparametric regression. The objective of this study was to estimate the nonparametric regression curve for longitudinal data using two combined estimators: truncated spline and local linear. The weighted least square method with a two-stage estimation procedure was used to obtain

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Liu, Chaolin, Hu Yang, and Jibo Wu. "On the Weighted Mixed Almost Unbiased Ridge Estimator in Stochastic Restricted Linear Regression." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/902715.

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We introduce the weighted mixed almost unbiased ridge estimator (WMAURE) based on the weighted mixed estimator (WME) (Trenkler and Toutenburg 1990) and the almost unbiased ridge estimator (AURE) (Akdeniz and Erol 2003) in linear regression model. We discuss superiorities of the new estimator under the quadratic bias (QB) and the mean square error matrix (MSEM) criteria. Additionally, we give a method about how to obtain the optimal values of parameterskandw. Finally, theoretical results are illustrated by a real data example and a Monte Carlo study.

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Adjekukor, A. J., and C. O. Aronu. "Robust Regression Estimation: A Doubly Weighted M-Estimation Approach with Generalized Jackknife Resampling." Asian Journal of Mathematics and Computer Research 32, no. 2 (2025): 27–35. https://doi.org/10.56557/ajomcor/2025/v32i29121.

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Robust regression estimation is crucial in addressing the influence of outliers and model misspecification in statistical modelling. This study proposes a Doubly Weighted M-Estimation (DWME) approach, integrating an adaptive weighting scheme with Generalized Jackknife Resampling (GJR) to enhance efficiency and robustness in parameter estimation. The DWME method incorporates case-specific and parameter-specific weighting functions, ensuring resistance against leverage points and heavy-tailed distributions. By leveraging GJR, the proposed estimator achieves reduced bias and variance while mainta

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Tao, Li, Lingnan Tai, and Maozai Tian. "Quantile regression for static panel data models with time-invariant regressors." PLOS ONE 18, no. 8 (2023): e0289474. http://dx.doi.org/10.1371/journal.pone.0289474.

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This paper proposes two new weighted quantile regression estimators for static panel data model with time-invariant regressors. The two new estimators can improve the estimation of the coefficients with time-invariant regressors, which are computationally convenient and simple to implement. Also, the paper shows consistency and asymptotic normality of the two proposed estimator for sequential and simultaneous N, T asymptotics. Monte Carlo simulation in various parameters sets proves the validity of the proposed approach. It has an empirical application to study the effects of the influence fac

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You, Jinhong, and Xian Zhou. "ASYMPTOTIC THEORY IN FIXED EFFECTS PANEL DATA SEEMINGLY UNRELATED PARTIALLY LINEAR REGRESSION MODELS." Econometric Theory 30, no. 2 (2013): 407–35. http://dx.doi.org/10.1017/s0266466613000352.

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This paper deals with statistical inference for the fixed effects panel data seemingly unrelated partially linear regression model. The model naturally extends the traditional fixed effects panel data regression model to allow for semiparametric effects. Multiple regression equations are permitted, and the model includes the aggregated partially linear model as a special case. A weighted profile least squares estimator for the parametric components is proposed and shown to be asymptotically more efficient than those neglecting the contemporaneous correlation. Furthermore, a weighted two-stage

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Yang, Hu, Xinfeng Chang, and Deqiang Liu. "Improvement of the Liu Estimator in Weighted Mixed Regression." Communications in Statistics - Theory and Methods 38, no. 2 (2009): 285–92. http://dx.doi.org/10.1080/03610920802192513.

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Li, Erqian, Jianxin Pan, Manlai Tang, et al. "Weighted Competing Risks Quantile Regression Models and Variable Selection." Mathematics 11, no. 6 (2023): 1295. http://dx.doi.org/10.3390/math11061295.

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The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selecti

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Gösta Andersson, Per. "A conditional perspective of weighted variance estimation of the optimal regression estimator." Journal of Statistical Planning and Inference 136, no. 1 (2006): 221–34. http://dx.doi.org/10.1016/j.jspi.2004.06.024.

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Budiantara, I. Nyoman. "APLIKASI SPLINE ESTIMATOR TERBOBOT." Jurnal Teknik Industri 3, no. 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) kurv

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Sukran, Ade Matao, I Nyoman Budiantara, and Vita Ratnasari. "The Curve Estimation Nonparametric Regression Multiresponse Mixed with Truncated Spline, Fourier Series, and Kernel." Mandalika Mathematics and Educations Journal 7, no. 2 (2025): 766–87. https://doi.org/10.29303/jm.v7i2.9188.

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This study formulates a nonparametric regression model for multiresponse data by combining three estimators: truncated spline, Fourier series, and kernel function. Each estimator captures specific characteristics. Truncated spline capture local traits with knot points, while fourier series capture periodic patterns and kernel estimators provide flexible smoothing for unknown functional forms. The model proposed is under an additive assumption where each predictor contributes independently to each response. Estimation is done with Weighted Least Squares (WLS) method which is efficient in managi

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Adamczyk, Tomasz. "Application of robust estimation methods in real estate valuation." Acta Scientiarum Polonorum Administratio Locorum 23, no. 4 (2024): 349–60. https://doi.org/10.31648/aspal.10726.

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Motives: Conducting real estate appraisals in well-developed markets presents a multitude of data analysis challenges. Some property price data may contain outliers that can significantly affect the valuation process and, as a result, the estimated value. In the case of real estate valuation regression models, estimation is most often based on the least squares method, where outliers are taken into account just like the rest of the data. Eliminating or minimizing the influence of outliers can lead to more reliable estimation results. Such problems can be solved by implementing robust regressio

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Marx, Brian D., and Eric P. Smith. "Weighted Multicollinearity in Logistic Regression: Diagnostics and Biased Estimation Techniques with an Example from Lake Acidification." Canadian Journal of Fisheries and Aquatic Sciences 47, no. 6 (1990): 1128–35. http://dx.doi.org/10.1139/f90-131.

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An historical data set from the Adirondack region of New York is revisited to study the relationship between water chemistry variables associated with acid precipitation and the presence/absence of brook trout (Salvelinus fontinalis) and lake trout (Salvelinus namaycush). For the trout species data sets, water chemistry variables associated with acid precipitation, for example pH and alkalinity, are highly correlated. Regression models to assess their effects on the probability of the presence of fish species are therefore affected by multicollinearity. Because the appropriate regressions are

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Liang, Han-Ying, and Bing-Yi Jing. "Strong Consistency of Estimators for Heteroscedastic Partly Linear Regression Model under Dependent Samples." Journal of Applied Mathematics and Stochastic Analysis 15, no. 3 (2002): 207–19. http://dx.doi.org/10.1155/s1048953302000187.

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In this paper we are concerned with the heteroscedastic regression model yi=xiβ+g(ti)+σiei, 1≤i≤n under correlated errors ei, where it is assumed that σi2=f(ui), the design points (xi,ti,ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance ei are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator.

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Zhao, Pei Xin. "Quantile Regression for Partially Linear Models with Missing Responses at Random." Applied Mechanics and Materials 727-728 (January 2015): 1013–16. http://dx.doi.org/10.4028/www.scientific.net/amm.727-728.1013.

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In this paper, we propose a weighted quantile regression method for partially linear models with missing response at random. The proposed estimation method can give an efficient estimator for parametric components, and can attenuate the effect of missing responses. Some simulations are carried out to assess the performance of the proposed estimation method, and simulation results indicate that the proposed method is workable.

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Alshqaq, Shokrya S., Abdullah A. Ahmadini, and Ali H. Abuzaid. "Some New Robust Estimators for Circular Logistic Regression Model with Applications on Meteorological and Ecological Data." Mathematical Problems in Engineering 2021 (May 25, 2021): 1–15. http://dx.doi.org/10.1155/2021/9944363.

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Maximum likelihood estimation ( MLE ) is often used to estimate the parameters of the circular logistic regression model due to its efficiency under a parametric model. However, evidence has shown that the classical MLE extremely affects the parameter estimation in the presence of outliers. This article discusses the effect of outliers on circular logistic regression and extends four robust estimators, namely, Mallows, Schweppe, Bianco and Yohai estimator BY , and weighted BY estimators, to the circular logistic regression model. These estimators have been successfully used in linear logistic

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Ohyver, Margaretha, Purhadi, and Achmad Choiruddin. "Parameter Estimation of Geographically and Temporally Weighted Elastic Net Ordinal Logistic Regression." Mathematics 13, no. 8 (2025): 1345. https://doi.org/10.3390/math13081345.

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Geographically and Temporally Weighted Elastic Net Ordinal Logistic Regression is a parsimonious ordinal logistic regression with consideration of the existence of spatial and temporal effects. This model has been developed with the following three considerations: the spatial effect, the temporal effect, and predictor selection. The last point prompted the use of Elastic Net regularization in choosing predictors while handling multicollinearity, which often arises when there are many predictors involved. The Elastic Net penalty combines ridge and LASSO penalties, leading to the determination o

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Alheety, Mustafa Ismaeel Naif. "New Versions of Liu-type Estimator in Weighted and non-weighted Mixed Regression Model." Baghdad Science Journal 17, no. 1(Suppl.) (2020): 0361. http://dx.doi.org/10.21123/bsj.2020.17.1(suppl.).0361.

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This paper considers and proposes new estimators that depend on the sample and on prior information in the case that they either are equally or are not equally important in the model. The prior information is described as linear stochastic restrictions. We study the properties and the performances of these estimators compared to other common estimators using the mean squared error as a criterion for the goodness of fit. A numerical example and a simulation study are proposed to explain the performance of the estimators.

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Sholiha, Anisatus, Kuzairi Kuzairi, and M. Fariz Fadillah Madianto. "Estimator Deret Fourier Dalam Regresi Nonparametrik dengan Pembobot Untuk Perencanaan Penjualan Camilan Khas Madura." Zeta - Math Journal 4, no. 1 (2018): 18–23. http://dx.doi.org/10.31102/zeta.2018.4.1.18-23.

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The purpose of regression analysis is determining the relationship between response variables to predictor variables. To estimate the regression curve there are three approaches, parametric regression, nonparametric regression, and semiparametric regression. In this study, the estimator form of nonparametric regression curve is analyzed by using the Fourier series approach with sine and cosine bases, sine bases, and cosine bases. Based on Weighted Least Square (WLS) optimization, the estimator result can be applied to model the sale planning of Madura typical snacks. Nonparametric regression e

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Lendle, Samuel David, Bruce Fireman, and Mark J. van der Laan. "Balancing Score Adjusted Targeted Minimum Loss-based Estimation." Journal of Causal Inference 3, no. 2 (2015): 139–55. http://dx.doi.org/10.1515/jci-2012-0012.

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AbstractAdjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-bas

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Li, Yang, Le Qi, Yichen Qin, Cunjie Lin, and Yuhong Yang. "Block Weighted Least Squares Estimation for Nonlinear Cost-based Split Questionnaire Design." Journal of Official Statistics 39, no. 4 (2023): 459–87. http://dx.doi.org/10.2478/jos-2023-0022.

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Abstract In this study, we advocate a two-stage framework to deal with the issues encountered in surveys with long questionnaires. In Stage I, we propose a split questionnaire design (SQD) developed by minimizing a quadratic cost function while achieving reliability constraints on estimates of means, which effectively reduces the survey cost, alleviates the burden on the respondents, and potentially improves data quality. In Stage II, we develop a block weighted least squares (BWLS) estimator of linear regression coefficients that can be used with data obtained from the SQD obtained in Stage I

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Wang, C. Y., and Hua Yun Chen. "Augmented Inverse Probability Weighted Estimator for Cox Missing Covariate Regression." Biometrics 57, no. 2 (2001): 414–19. http://dx.doi.org/10.1111/j.0006-341x.2001.00414.x.

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