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Journal articles on the topic 'Ordinary least squares method'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Machado, Vieira Filho, and de Oliveira. "Forensic Speaker Verification Using Ordinary Least Squares." Sensors 19, no. 20 (October 10, 2019): 4385. http://dx.doi.org/10.3390/s19204385.

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In Brazil, the recognition of speakers for forensic purposes still relies on a subjectivity-based decision-making process through a results analysis of untrustworthy techniques. Owing to the lack of a voice database, speaker verification is currently applied to samples specifically collected for confrontation. However, speaker comparative analysis via contested discourse requires the collection of an excessive amount of voice samples for a series of individuals. Further, the recognition system must inform who is the most compatible with the contested voice from pre-selected individuals. Accordingly, this paper proposes using a combination of linear predictive coding (LPC) and ordinary least squares (OLS) as a speaker verification tool for forensic analysis. The proposed recognition technique establishes confidence and similarity upon which to base forensic reports, indicating verification of the speaker of the contested discourse. Therefore, in this paper, an accurate, quick, alternative method to help verify the speaker is contributed. After running seven different tests, this study preliminarily achieved a hit rate of 100% considering a limited dataset (Brazilian Portuguese). Furthermore, the developed method extracts a larger number of formants, which are indispensable for statistical comparisons via OLS. The proposed framework is robust at certain levels of noise, for sentences with the suppression of word changes, and with different quality or even meaningful audio time differences.

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2

Watagoda, Lasanthi C. R. Pelawa. "A Sub-Model Theorem for Ordinary Least Squares." International Journal of Statistics and Probability 8, no. 1 (November 19, 2018): 40. http://dx.doi.org/10.5539/ijsp.v8n1p40.

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Variable selection or subset selection is an important step in the process of model fitting. There are many ways to select the best subset of variables including Forward selection, Backward elimination, etcetera. Ordinary least squares (OLS) is one of the most commonly used methods of fitting the final model. Final sub-model can perform poorly if the variable selection process failed to choose the right number of variables. This paper gives a new theorem and a mathematical proof to illustrate the reason for the poor performances, when using the least squares method after variable selection.

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3

Sanchez, Juan. "Estimating Detection Limits in Chromatography from Calibration Data: Ordinary Least Squares Regression vs. Weighted Least Squares." Separations 5, no. 4 (October 8, 2018): 49. http://dx.doi.org/10.3390/separations5040049.

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It is necessary to determine the limit of detection when validating any analytical method. For methods with a linear response, a simple and low labor-consuming procedure is to use the linear regression parameters obtained in the calibration to estimate the blank standard deviation from the residual standard deviation (sres), or the intercept standard deviation (sb0). In this study, multiple experimental calibrations are evaluated, applying both ordinary and weighted least squares. Moreover, the analyses of replicated blank matrices, spiked at 2–5 times the lowest calculated limit values with the two regression methods, are performed to obtain the standard deviation of the blank. The limits of detection obtained with ordinary least squares, weighted least squares, the signal-to-noise ratio, and replicate blank measurements are then compared. Ordinary least squares, which is the simplest and most commonly applied calibration regression methodology, always overestimate the values of the standard deviations at the lower levels of calibration ranges. As a result, the detection limits are up to one order of magnitude greater than those obtained with the other approaches studied, which all gave similar limits.

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4

de Souza, Scheilla V. C., and Roberto G. Junqueira. "A procedure to assess linearity by ordinary least squares method." Analytica Chimica Acta 552, no. 1-2 (November 2005): 25–35. http://dx.doi.org/10.1016/j.aca.2005.07.043.

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5

YUKUTAKE, Kiyoshi, and Atsushi YOSHIMOTO. "Analysis of Lumber Demand and Supply in Japan : Price Elasticities by the Ordinary Least Squares Method, Two Stage Least Squares Method and Three Stage Least Squares Method." Japanese Journal of Forest Planning 36, no. 2 (2002): 81–98. http://dx.doi.org/10.20659/jjfp.36.2_81.

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6

Yanuar, Ferra. "The Simulation Study to Test the Performance of Quantile Regression Method With Heteroscedastic Error Variance." CAUCHY 5, no. 1 (November 30, 2017): 36. http://dx.doi.org/10.18860/ca.v5i1.4209.

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<div><p class="Keywords">The purpose of this article was to describe the ability of the quantile regression method in overcoming the violation of classical assumptions. The classical assumptions that are violated in this study are variations of non-homogeneous error or heteroscedasticity. To achieve this goal, the simulated data generated with the design of certain data distribution. This study did a comparison between the models resulting from the use of the ordinary least squares and the quantile regression method to the same simulated data. Consistency of both methods was compared with conducting simulation studies as well. This study proved that the quantile regression method had standard error, confidence interval width and mean square error (MSE) value smaller than the ordinary least squares method. Thus it can be concluded that the quantile regression method is able to solve the problem of heteroscedasticity and produce better model than the ordinary least squares. In addition the ordinary least squares is not able to solve the problem of heteroscedasticity.</p></div>

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7

Weiss, Andrew A. "A Comparison of Ordinary Least Squares and Least Absolute Error Estimation." Econometric Theory 4, no. 3 (December 1988): 517–27. http://dx.doi.org/10.1017/s0266466600013438.

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In a linear-regression model with heteroscedastic errors, we consider two tests: a Hausman test comparing the ordinary least squares (OLS) and least absolute error (LAE) estimators and a test based on the signs of the errors from OLS. It turns out that these are related by the well-known equivalence between Hausman and the generalized method of moments tests. Particular cases, including homoscedasticity and asymmetry in the errors, are discussed.

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8

Wang, Song-Gui, Shein-Chung Chow, and Siu-Keung Tse. "On ordinary least-squares methods for sample surveys." Statistics & Probability Letters 20, no. 3 (June 1994): 173–82. http://dx.doi.org/10.1016/0167-7152(94)90039-6.

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9

Cunia, T., and R. D. Briggs. "Forcing additivity of biomass tables: use of the generalized least squares method." Canadian Journal of Forest Research 15, no. 1 (February 1, 1985): 23–28. http://dx.doi.org/10.1139/x85-006.

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The generalized least squares procedure is applied to sample tree data for which additive biomass tables are required. This procedure is proposed as an alternative to the ordinary weighted least squares in order to account for the fact that several biomass components are measured on the same sample trees. The biomass tables generated by the generalized and the ordinary least squares are very similar, the confidence intervals are sometimes wider, sometimes narrower, but the prediction intervals are always narrower for the generalized least squares method.

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10

Long, Rebecca G. "The Crux of the Method: Assumptions in Ordinary Least Squares and Logistic Regression." Psychological Reports 103, no. 2 (October 2008): 431–34. http://dx.doi.org/10.2466/pr0.103.2.431-434.

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Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.

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11

Yurdakul, Funda. "Correlations between energy consumption per capita, growth rate, industrialisation, trade volume and urbanisation: the case of Turkey." New Trends and Issues Proceedings on Humanities and Social Sciences 4, no. 10 (January 12, 2018): 118–27. http://dx.doi.org/10.18844/prosoc.v4i10.3085.

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This study examines the relationship of energy consumption per capita with growth rate, industrialisation, trade volume and urbanisation in Turkish economy throughout the 1980–2015 period using the Engle-Granger, Fully modified ordinary least squares (FMOLS), canonical cointegration regression (CCR) and dynamic ordinary least squares (DOLS) methods. Analysis results revealed a long-run equilibrium relationship between the change in energy consumption per capita and growth rate, industrialisation, trade volume and urbanisation. Urbanisation, industrialisation, growth rate and trade volume positively influence the change in energy consumption per capita. Keywords: Energy consumption, Engle-Granger method, fully modified ordinary least squares (FMOLS) method, canonical cointegration regression (CCR), dynamic ordinary least squares (DOLS) method.

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12

Yeniay, Özgür, Öznur İşçi, Atilla Göktaş, and M. Niyazi Çankaya. "Time Scale in Least Square Method." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/354237.

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Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.

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13

Abdelhadi, Yaser. "Linear modeling and regression for exponential engineering functions by a generalized ordinary least squares method." International Journal of Engineering & Technology 3, no. 2 (April 20, 2014): 174. http://dx.doi.org/10.14419/ijet.v3i2.2023.

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Linear transformations are performed for selected exponential engineering functions. The Optimum values of parameters of the linear model equation that fits the set of experimental or simulated data points are determined by the linear least squares method. The classical and matrix forms of ordinary least squares are illustrated. Keywords: Exponential Functions; Linear Modeling; Ordinary Least Squares; Parametric Estimation; Regression Steps.

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14

Cunia, T., and R. D. Briggs. "Harmonizing biomass tables by generalized least squares." Canadian Journal of Forest Research 15, no. 2 (April 1, 1985): 331–40. http://dx.doi.org/10.1139/x85-054.

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To construct biomass tables for various tree components that are consistent with each other, one may use linear regression techniques with dummy variables. When the biomass of these components is measured on the same sample trees, one should also use the generalized rather than ordinary least squares method. A procedure is shown which allows the estimation of the covariance matrix of the sample biomass values and circumvents the problem of storing and inverting large covariance matrices. Applied to 20 sets of sample tree data, the generalized least squares regressions generated estimates which, on the average were slightly higher (about 1%) than the sample data. The confidence and prediction bands about the regression function were wider, sometimes considerably wider than those estimated by the ordinary weighted least squares.

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15

Pedraza-Yepes, Cristian, Jose Daniel Hernandez-Vasquez, Fernando Pastor Forero, Leonardo Perez Manotas, and Jorge Gonzalez-Coneo. "Metrological evaluation of a bourdon manometer from the ordinary least squares method." Contemporary Engineering Sciences 11, no. 94 (2018): 4681–89. http://dx.doi.org/10.12988/ces.2018.88482.

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16

Enjarwati, Tria. "IMPACT OF GOVERNMENT FISCAL SPACE AND MANPOWER TO THE GROSS DOMESTIC PRODUCTS OF INDONESIA PERIOD 1990-2015." Journal of Developing Economies 3, no. 1 (July 31, 2018): 20. http://dx.doi.org/10.20473/jde.v3i1.8562.

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To purpose of this study was to examine and analyze the effect of fiscal space and labour absorption to Indonesia Gross Domestic Product (GDP) within period 1990-2015. This study uses the least squares method or Ordinary Least Square (OLS) with time series data. Variables used in this study is the Gross Domestic Product (GDP) as the dependent variable, whereas for independent variables using the fiscal space and labour absorption. The results of regression calculations using the least squares method or Ordinary Least Square (OLS) in this study indicate that the fiscal space variable has a positive significant effect, and labour absorption variable has a positive significant effect to indonesia Gross Domestic Product (GDP).

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17

Mahaboob, B., B. Venkateswarlu, C. Narayana, J. Ravi sankar, and P. Balasiddamuni. "A Treatise on Ordinary Least Squares Estimation of Parameters of Linear Model." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 518. http://dx.doi.org/10.14419/ijet.v7i4.10.21216.

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This research article primarily focuses on the estimation of parameters of a linear regression model by the method of ordinary least squares and depicts Gauss-Mark off theorem for linear estimation which is useful to find the BLUE of a linear parametric function of the classical linear regression model. A proof of generalized Gauss-Mark off theorem for linear estimation has been presented in this memoir. Ordinary Least Squares (OLS) regression is one of the major techniques applied to analyse data and forms the basics of many other techniques, e.g. ANOVA and generalized linear models [1]. The use of this method can be extended with the use of dummy variable coding to include grouped explanatory variables [2] and data transformation models [3]. OLS regression is particularly powerful as it relatively easy to check the model assumption such as linearity, constant, variance and the effect of outliers using simple graphical methods [4]. J.T. Kilmer et.al [5] applied OLS method to evolutionary and studies of algometry.

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18

HUANG, J. W., L. MA, and R. LI. "STUDY ON MEASUREMENT RELIABILITY BASED ON LIU ESTIMATOR." Latin American Applied Research - An international journal 48, no. 3 (July 31, 2018): 187–92. http://dx.doi.org/10.52292/j.laar.2018.224.

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In this paper, we introduce the Liu estimator in the measurement process as an alternative method to the ordinary least squares estimator. To compare the Liu estimator and the ordinary least squares estimator under the reliability criterion, a simulation study is conducted. Simulation study results show that Liu estimator is an effective method to replace OLS estimator in process measurement. When the Liu parameter choose in a reasonable range, Liu estimator superior to ordinary least squares estimator in terms of reliability.

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19

Rzhetsky, Andrey, and Masatoshi Nei. "Statistical properties of the ordinary least-squares, generalized least-squares, and minimum-evolution methods of phylogenetic inference." Journal of Molecular Evolution 35, no. 4 (October 1992): 367–75. http://dx.doi.org/10.1007/bf00161174.

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20

LONG, REBECCA G. "THE CRUX OF THE METHOD: ASSUMPTIONS IN ORDINARY LEAST SQUARES AND LOGISTIC REGRESSION." Psychological Reports 103, no. 6 (2008): 431. http://dx.doi.org/10.2466/pr0.103.6.431-434.

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21

TANG, HENGJIN, and SADAAKI MIYAMOTO. "SEQUENTIAL EXTRACTION OF FUZZY REGRESSION MODELS: LEAST SQUARES AND LEAST ABSOLUTE DEVIATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19, supp01 (December 2011): 53–63. http://dx.doi.org/10.1142/s0218488511007349.

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Fuzzy c-regression models are known to be useful in real applications, but there are two drawbacks: strong dependency on the predefined number of clusters and sensitiveness against outliers or noises. To avoid these drawbacks, we propose sequential fuzzy regression models based on least absolute deviations which we call SFCRMLAD. This algorithm sequentially extracts one cluster at a time using a method of noise-detection, enabling the automatic determination of clusters and having robustness to noises. We compare this method with the ordinary fuzzy c-regression models based on least squares, fuzzy c-regression models based on least absolute deviations, and moreover sequential fuzzy regression models based on least squares. For this purpose we use a two-dimensional illustrative example whereby characteristics of the four methods are made clear. Moreover a simpler and more efficient algorithm of SFCRMLAD can be used for scalar input and output variables, while a general algorithm of SFCRMLAD uses linear programming solutions for multivariable input. By using the above example, we compare efficiency of different algorithms.

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22

Huang, Zhiyong, Ziyan Luo, and Naihua Xiu. "High-Dimensional Least-Squares with Perfect Positive Correlation." Asia-Pacific Journal of Operational Research 36, no. 04 (August 2019): 1950016. http://dx.doi.org/10.1142/s0217595919500167.

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The least-squares is a common and important method in linear regression. However, it often leads to overfitting phenomenon as dealing with high-dimensional problems, and various regularization schemes regarding prior information for specific problems are studied to make up such a deficiency. In the sense of Kendall’s [Formula: see text] from the community of nonparametric analysis, we establish a new model wherein the ordinary least-squares is equipped with perfect positive correlation constraint, sought to maintain the concordance of the rankings of the observations and the systematic components. By sorting the observations into an ascending order, we reduce the perfect positive correlation constraint into a linear inequality system. The resulting linearly constrained least-squares problem together with its dual problem is shown to be solvable. In particular, we introduce a mild assumption on the observations and the measurement matrix which rules out the zero vector from the optimal solution set. This indicates that our proposed model is statistically meaningful. To handle large-scale instances, we propose an efficient alternating direction method of multipliers (ADMM) to solve the proposed model from the dual perspective. The effectiveness of our model compared to ordinary least-squares is evaluated in terms of rank correlation coefficient between outputs and the systematic components, and the efficiency of our dual algorithm is demonstrated with the comparison to three efficient solvers via CVX in terms of computation time, solution accuracy and rank correlation coefficient.

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23

Xi, F., D. Nancoo, and G. Knopf. "Total Least-Squares Methods for Active View Registration of Three-Dimensional Line Laser Scanning Data." Journal of Dynamic Systems, Measurement, and Control 127, no. 1 (March 25, 2004): 50–56. http://dx.doi.org/10.1115/1.1876492.

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In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.

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24

Haupt, Harry, Friedrich Lösel, and Mark Stemmler. "Quantile Regression Analysis and Other Alternatives to Ordinary Least Squares Regression." Methodology 10, no. 3 (January 1, 2014): 81–91. http://dx.doi.org/10.1027/1614-2241/a000077.

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Data analyses by classical ordinary least squares (OLS) regression techniques often employ unrealistic assumptions, fail to recognize the source and nature of heterogeneity, and are vulnerable to extreme observations. Therefore, this article compares robust and non-robust M-estimator regressions in a statistical demonstration study. Data from the Erlangen-Nuremberg Development and Prevention Project are used to model risk factors for physical punishment by fathers of 485 elementary school children. The Corporal Punishment Scale of the Alabama Parenting Questionnaire was the dependent variable. Fathers’ aggressiveness, dysfunctional parent-child relations, various other parenting characteristics, and socio-demographic variables served as predictors. Robustness diagnostics suggested the use of trimming procedures and outlier diagnostics suggested the use of robust estimators as an alternative to OLS. However, a quantile regression analysis provided more detailed insights beyond the measures of central tendency and detected sources of considerable heterogeneity in the risk structure of father’s corporal punishment. Advantages of this method are discussed with regard to methodological and content issues.

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25

Bilginol, Kübra, Hayri Hakan Denli, and Dursun Zafer Şeker. "Ordinary Least Squares Regression Method Approach for Site Selection of Automated Teller Machines (ATMs)." Procedia Environmental Sciences 26 (2015): 66–69. http://dx.doi.org/10.1016/j.proenv.2015.05.026.

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26

Mouco, A., and A. Abur. "Improving the wide-area PMU-based fault location method using ordinary least squares estimation." Electric Power Systems Research 189 (December 2020): 106620. http://dx.doi.org/10.1016/j.epsr.2020.106620.

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27

Mukhopadhyay, Parimal, and Rainer Schwabe. "On the performance of the ordinary least squares method under an error component model." Metrika 47, no. 1 (January 1998): 215–26. http://dx.doi.org/10.1007/bf02742874.

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28

De-Graft Acquah, Henry. "Comparing ols and rank-based estimation techniques for production analysis: An application to Ghanaian maize farms." Applied Studies in Agribusiness and Commerce 10, no. 4-5 (December 31, 2016): 125–30. http://dx.doi.org/10.19041/apstract/2016/4-5/16.

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This paper introduces the rank-based estimation method to modelling the Cobb-Douglas production function as an alternative to the least squares approach. The intent is to demonstrate how a nonparametric regression based on a rank-based estimator can be used to estimate a Cobb-Douglas production function using data on maize production from Ghana. The nonparametric results are compared to common parametric specification using the ordinary least squares regression. Results of the study indicate that the estimated coefficients of the CobbDouglas Model using the Least squares method and the rank-based regression analysis are similar. Findings indicated that in both estimation techniques, land and Equipment had a significant and positive influence on output whilst agrochemicals had a significantly negative effect on output. Additionally, seeds which also had a negative influence on output was found to be significant in the robust rank-based estimation, but insignificant in the ordinary least square estimation. Both the least squares and rank-based regression suggest that the farmers were operating at an increasing returns to scale. In effect this paper demonstrate the usefulness of the rank-based estimation in production analysis. JEL CODE: Q18, D24, Q12, C1 and C67

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29

Wu, Jibo. "Comparison of Some Estimators under the Pitman’s Closeness Criterion in Linear Regression Model." Journal of Applied Mathematics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/654949.

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Batah et al. (2009) combined the unbiased ridge estimator and principal components regression estimator and introduced the modifiedr-kclass estimator. They also showed that the modifiedr-kclass estimator is superior to the ordinary least squares estimator and principal components regression estimator in the mean squared error matrix. In this paper, firstly, we will give a new method to obtain the modifiedr-kclass estimator; secondly, we will discuss its properties in some detail, comparing the modifiedr-kclass estimator to the ordinary least squares estimator and principal components regression estimator under the Pitman closeness criterion. A numerical example and a simulation study are given to illustrate our findings.

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LI, JIANPING, ZHENYU CHEN, LIWEI WEI, WEIXUAN XU, and GANG KOU. "FEATURE SELECTION VIA LEAST SQUARES SUPPORT FEATURE MACHINE." International Journal of Information Technology & Decision Making 06, no. 04 (December 2007): 671–86. http://dx.doi.org/10.1142/s0219622007002733.

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In many applications such as credit risk management, data are represented as high-dimensional feature vectors. It makes the feature selection necessary to reduce the computational complexity, improve the generalization ability and the interpretability. In this paper, we present a novel feature selection method — "Least Squares Support Feature Machine" (LS-SFM). The proposed method has two advantages comparing with conventional Support Vector Machine (SVM) and LS-SVM. First, the convex combinations of basic kernels are used as the kernel and each basic kernel makes use of a single feature. It transforms the feature selection problem that cannot be solved in the context of SVM to an ordinary multiple-parameter learning problem. Second, all parameters are learned by a two stage iterative algorithm. A 1-norm based regularized cost function is used to enforce sparseness of the feature parameters. The "support features" refer to the respective features with nonzero feature parameters. Experimental study on some of the UCI datasets and a commercial credit card dataset demonstrates the effectiveness and efficiency of the proposed approach.

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Prime, Sunantha. "Forecasting the changes in daily stock prices in Shanghai Stock Exchange using Neural Network and Ordinary Least Squares Regression." Investment Management and Financial Innovations 17, no. 3 (October 1, 2020): 292–307. http://dx.doi.org/10.21511/imfi.17(3).2020.22.

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The research focuses on finding a superior forecasting technique to predict stock movement and behavior in the Shanghai Stock Exchange. The author’s interest is in stock market activities during high volatility, specifically 13 years from 2002 to 2015. This volatile period, fueled by events such as the dot-com bubble, SARS outbreak, political leadership transitions, and the global financial crisis, is of interest. The study aims to analyze changes in stock prices during an unstable period. The author used advanced computer sciences, Machine Learning through information processing and training, and the traditional statistical approach, the Multiple Linear Regression Model, with the least square method. Both techniques are accurate predictors measured by Absolute Percent Error with a range of 1.50% to 1.65%, using a data file containing 3,283 observations generated to record the daily close prices of individual Chinese companies. The t-test paired difference experiment shows the superiority of Neural Network in the finance sector and potentially not in other sectors. The Multiple Linear Regression Model performs equivalent to the Neural Network in other sectors.

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Ivanov, Dmitriy V., Ilya L. Sandler, and Natalya V. Chertykovtseva. "Estimation of Parameters of Hyperbolic Functions with Additive Noise." Advances in Science and Technology 105 (April 2021): 302–8. http://dx.doi.org/10.4028/www.scientific.net/ast.105.302.

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Hyperbolic functions are widely used to write solutions to ordinary differential equations and partial differential equations. These functions are nonlinear in parameters, which makes it difficult to estimate the parameters of these functions. In the paper, two-step algorithms for estimating the parameters of hyperbolic sine and cosine (sinh and cosh) in the presence of measurement errors are proposed. At the first step, the hyperbolic function is transformed into a linear difference equation (autoregression) of the second order. Estimation in the presence of noise of observation of autoregression parameters using ordinary least square (OLS) gives biased estimates. Modifications of the two-stage estimation algorithm based on the use of the method of total least squares (TLS) and the method of extended instrumental variables (EIV), hyperbolic sine and cosine in the presence of errors in measurements are proposed. Numerical experiments have shown that the accuracy of the parameter estimation using the proposed modifications is higher than the accuracy of the estimate obtained using the ordinary least squares method (OLS).

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Lu, Yuan, and Xiang Hong Cheng. "Non-Linear Least Squares Large Misalignment Estimation in Transfer Alignment." Advanced Materials Research 989-994 (July 2014): 1962–68. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.1962.

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Large misalignment is unavoidable for subsystems which could be deployed randomly on the carriers such as shipborne aircrafts, AUV. Ordinary linear filtering algorithms don’t converge fast and accurately in non-linear conditions. It's critical for the accuracy of the transfer alignment. In this paper, a new misalignment and gyroscope bias online estimation method based on angular velocity processing is presented. Sensor measurements of M-SINS and S-SINS will be recorded for a certain period. Misalignment and the gyroscope bias will be calculated from these measurements directly with non-linear least square algorithm. Trust region method with pre-conditioning, subspace and conjugate gradient are applied for faster converge and better accuracy. Simulation results demonstrate the effectiveness of the algorithm.

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Morley, Clive L. "A Comparison of Three Methods for Estimating Tourism Demand Models." Tourism Economics 2, no. 3 (September 1996): 223–34. http://dx.doi.org/10.1177/135481669600200302.

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Estimation of tourism demand models involves a set of related equations with errors which may not satisfy the common assumptions of regression modelling. Results from a simulation exercise show that, for the error types and small samples considered, the Generalized Method of Moments is less accurate on average than the Ordinary Least Squares and Seemingly Unrelated Regression methods, which had very similar accuracies. Overall, the Ordinary Least Squares technique performs well and the results give little reason to use the more complex estimation techniques.

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Beck, Nathaniel, and Jonathan N. Katz. "Nuisance vs. Substance: Specifying and Estimating Time-Series-Cross-Section Models." Political Analysis 6 (1996): 1–36. http://dx.doi.org/10.1093/pan/6.1.1.

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In a previous article we showed that ordinary least squares with panel corrected standard errors is superior to the Parks generalized least squares approach to the estimation of time-series-cross-section models. In this article we compare our proposed method with another leading technique, Kmenta's “cross-sectionally heteroskedastic and timewise autocorrelated” model. This estimator uses generalized least squares to correct for both panel heteroskedasticity and temporally correlated errors. We argue that it is best to model dynamics via a lagged dependent variable rather than via serially correlated errors. The lagged dependent variable approach makes it easier for researchers to examine dynamics and allows for natural generalizations in a manner that the serially correlated errors approach does not. We also show that the generalized least squares correction for panel heteroskedasticity is, in general, no improvement over ordinary least squares and is, in the presence of parameter heterogeneity, inferior to it. In the conclusion we present a unified method for analyzing time-series-cross-section data.

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Annan, Richard Fiifi, Yao Yevenyo Ziggah, John Ayer, and Christian Amans Odutola. "ACCURACY ASSESSMENT OF HEIGHTS OBTAINED FROM TOTAL STATION AND LEVEL INSTRUMENT USING TOTAL LEAST SQUARES AND ORDINARY LEAST SQUARES METHODS." Geoplanning: Journal of Geomatics and Planning 3, no. 2 (October 25, 2016): 87. http://dx.doi.org/10.14710/geoplanning.3.2.87-92.

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Spirit levelling has been the traditional means of determining Reduced Levels (RL’s) of points by most surveyors. The assertion that the level instrument is the best instrument for determining elevations of points needs to be reviewed; this is because technological advancement is making the total station a very reliable tool for determining reduced levels of points. In order to achieve the objective of this research, reduced levels of stations were determined by a spirit level and a total station instrument. Ordinary Least Squares (OLS) and Total Least Squares (TLS) techniques were then applied to adjust the level network. Unlike OLS which considers errors only in the observation matrix, and adjusts observations in order to make the sum of its residuals minimum, TLS considers errors in both the observation matrix and the data matrix, thereby minimising the errors in both matrices. This was evident from the results obtained in this study such that OLS approximated the adjusted reduced levels, which compromises accuracy, whereas the opposite happened in the TLS adjustment results. Therefore, TLS was preferred to OLS and Analysis of Variance (ANOVA) was performed on the preferred TLS solution and the RL’s from the total station in order to ascertain how accurate the total station can be relative to the spirit level.

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Dai, Heping, and Naresh K. Sinha. "A Robust Off-Line Method for System Identification: Robust Iterative Least Squares Method With Modified Residuals." Journal of Dynamic Systems, Measurement, and Control 113, no. 4 (December 1, 1991): 597–603. http://dx.doi.org/10.1115/1.2896463.

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A general criterion is proposed for robust identification of both linear and bilinear systems. Following Huber’s minimax principle, the ordinary iterative Gauss-Newton approach is applied, with modified residuals, to minimize the suggested robust cost function. The proposed method, named the robust iterative least squares method with modified residuals (RILSMMR), can provide simultaneously robust estimates of the system parameters as well as the residual variance. Therefore it is superior to the earlier robust methods. A proof of convergence of the RILSMMR is given. Results of simulation with both the RILSMMR and nonrobust identification methods are included. These confirm that RILSMMR has certain advantages over both conventional nonrobust identification methods, as well as earlier robust methods.

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Shen, Gao Zhan, Tao Zhang, Ying Xu, and Yan Xing Wei. "Research and Experiment on Nonlinear Correction Algorithm of Metal Tube Rotameter." Advanced Materials Research 301-303 (July 2011): 1123–27. http://dx.doi.org/10.4028/www.scientific.net/amr.301-303.1123.

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The calibration curve of some metal tube rotameter has the characteristic of mutation. If the nonlinear least square method is still used as the method of linear correction, it will increase the measurement error and reduce the measurement accuracy. This paper presents a Division Ordinary Least Squares Method, which can reduce errors and improve accuracy. By the algorithm comparative experiment it can be proved that the method can improve the measurement accuracy.

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Marvuglia, Antonino, Maurizio Cellura, and Marcello Pucci. "A Generalization of the Orthogonal Regression Technique for Life Cycle Inventory." International Journal of Agricultural and Environmental Information Systems 3, no. 1 (January 2012): 51–71. http://dx.doi.org/10.4018/jaeis.2012010105.

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Life cycle assessment (LCA) is a method used to quantify the environmental impacts of a product, process, or service across its whole life cycle. One of the problems occurring when the system at hand involves processes delivering more than one valuable output is the apportionment of resource consumption and environmental burdens in the correct proportion amongst the products. The mathematical formulation of the problem is represented by the solution of an over-determined system of linear equations. The paper describes the application of an iterative algorithm for the implementation of least square regression to solve this over-determined system directly in its rectangular form. The applied algorithm dynamically passes from an Ordinary Least Squares (OLS) problem to the regression problems known as Total Least Squares (TLS) and Data Least Squares (DLS). The obtained results suggest further investigations. In particular, the so called constrained least squares method is identified as an interesting development of the methodology.

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Morley, Clive L. "An Evaluation of the Use of Ordinary Least Squares for Estimating Tourism Demand Models." Journal of Travel Research 35, no. 4 (April 1997): 69–73. http://dx.doi.org/10.1177/004728759703500411.

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Estimating tourism demand models involves a set of related equations with errors that may not satisfy the common assumptions of being independent, with constant variance and normal distribution. In such circumstances, seemingly unrelated regression estimation may be considered a better estimation technique than ordinary least squares. Results from a simulation exercise, however, show that generally there is little difference between ordinary least squares and seemingly unrelated regression. The ordinary least squares technique performs well, and the results give little reason to use more complex estimation techniques. Another feature of tourism data is that strong growth in tourist numbers is often observed. This feature implies that models in which such series are the dependent variable are not consistently estimated by least squares methods. A percentage error loss function is proposed as a more appropriate criterion for estimating tourist data of this type.

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Amihud, Yakov, and Clifford M. Hurvich. "Predictive Regressions: A Reduced-Bias Estimation Method." Journal of Financial and Quantitative Analysis 39, no. 4 (December 2004): 813–41. http://dx.doi.org/10.1017/s0022109000003227.

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AbstractStandard predictive regressions produce biased coefficient estimates in small samples when the regressors are Gaussian first-order autoregressive with errors that are correlated with the error series of the dependent variable. See Stambaugh (1999) for the single regressor model. This paper proposes a direct and convenient method to obtain reduced-bias estimators for single and multiple regressor models by employing an augmented regression, adding a proxy for the errors in the autoregressive model. We derive bias expressions for both the ordinary least-squares and our reduced-bias estimated coefficients. For the standard errors of the estimated predictive coefficients, we develop a heuristic estimator that performs well in simulations, for both the single predictor model and an important specification of the multiple predictor model. The effectiveness of our method is demonstrated by simulations and empirical estimates of common predictive models in finance. Our empirical results show that some of the predictive variables that were significant under ordinary least squares become insignificant under our estimation procedure.

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Wang, Xiaohui, and Weiguo Zhang. "Parameter Estimation for Long-Memory Stochastic Volatility at Discrete Observation." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/462982.

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Ordinary least squares estimators of variogram parameters in long-memory stochastic volatility are studied in this paper. We use the discrete observations for practical purposes under the assumption that the Hurst parameterH∈(1/2,1)is known. Based on the ordinary least squares method, we obtain both the explicit estimators for drift and diffusion by minimizing the distance function between the variogram and the data periodogram. Furthermore, the resulting estimators are shown to be consistent and to have the asymptotic normality. Numerical examples are also presented to illustrate the performance of our method.

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Kerkri, Abdelmounaim, Jelloul Allal, and Zoubir Zarrouk. "Robust Nonlinear Partial Least Squares Regression Using the BACON Algorithm." Journal of Applied Mathematics 2018 (October 2, 2018): 1–5. http://dx.doi.org/10.1155/2018/7696302.

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Partial least squares regression (PLS regression) is used as an alternative for ordinary least squares regression in the presence of multicollinearity. This occurrence is common in chemical engineering problems. In addition to the linear form of PLS, there are other versions that are based on a nonlinear approach, such as the quadratic PLS (QPLS2). The difference between QPLS2 and the regular PLS algorithm is the use of quadratic regression instead of OLS regression in the calculations of latent variables. In this paper we propose a robust version of QPLS2 to overcome sensitivity to outliers using the Blocked Adaptive Computationally Efficient Outlier Nominators (BACON) algorithm. Our hybrid method is tested on both real and simulated data.

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Et.al, Abdul Hadi Bhatti. "Least Square Methods Based on Control Points of Said Ball Curves for Solving Ordinary Differential Equations." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (April 11, 2021): 2597–607. http://dx.doi.org/10.17762/turcomat.v12i3.1261.

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This paper presents the use of Said Ball curve’s control points to approximate the solutions of linear ordinary differential equations (ODEs). Least squares methods (LSM) is proposed to find the control points of Said Ball curves by minimizing the error of residual function.The residual error is measured by taking the sum of squares of the Said Ball curve’s control points of the residual function. Then the approximate solution of ODEs is obtained by minimizing residual error.Two numerical examples are given in term of error and compared with the exact solution to demonstrate the efficiency of the proposed method.

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Mischke, C. R. "A New Approach for the Identification of a Regression Locus for Estimating CDF-Failure Equations on Rectified Plots." Journal of Vibration and Acoustics 109, no. 1 (January 1, 1987): 103–12. http://dx.doi.org/10.1115/1.3269382.

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In estimating the cumulative density function of data, investigators selectively transform the data and their order statistics in order to achieve rectification of the data string. Ordinary least-squares regression procedures no longer apply because of the transformations. Investigators are often seeking a fifty-percent (median) locus, which least-squares methods do not ordinarily discover. A weighted least-squares regression procedure is presented that will establish an estimate of the mean CDF line and through appropriate rotation, provide an estimate of the median CDF line. Examples from common distributions follow a general development.

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Liu, Qingfeng, and Andrey L. Vasnev. "A Combination Method for Averaging OLS and GLS Estimators." Econometrics 7, no. 3 (September 9, 2019): 38. http://dx.doi.org/10.3390/econometrics7030038.

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To avoid the risk of misspecification between homoscedastic and heteroscedastic models, we propose a combination method based on ordinary least-squares (OLS) and generalized least-squares (GLS) model-averaging estimators. To select optimal weights for the combination, we suggest two information criteria and propose feasible versions that work even when the variance-covariance matrix is unknown. The optimality of the method is proven under some regularity conditions. The results of a Monte Carlo simulation demonstrate that the method is adaptive in the sense that it achieves almost the same estimation accuracy as if the homoscedasticity or heteroscedasticity of the error term were known.

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Daniel, Farida. "MENGATASI PENCILAN PADA PEMODELAN REGRESI LINEAR BERGANDA DENGAN METODE REGRESI ROBUST PENAKSIR LMS." BAREKENG: Jurnal Ilmu Matematika dan Terapan 13, no. 3 (October 1, 2019): 145–56. http://dx.doi.org/10.30598/barekengvol13iss3pp145-156ar884.

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Ordinary Least Squares (OLS) is frequent used method for estimating parameters. OLS estimator is not a robust regression procedure for the presence of outliers, so the estimate becomes inappropriate. Least Median of Squares (LMS) is one of a robust estimator for the presence of outliers and has a high breakdown value. LMS estimate parameters by minimizing the median of squared residuals. Least Median of Squares (LMS) The purpose of this study is geting a regression equation that better than the regression equation before using OLS for the data that having outlier. For the first step, checking if there is outlier at data and then searching regression equation with LMS method. In this study used data stackloss and from estimation parameter of this data, LMS estimator showed better results compared to the OLS estimator because the regression equation from LMS method have smaller value of Mean Absolute Percentage Error (MAPE).

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كوركيس, حازم منصور. "Use the method of parsing anomalous valueIn estimating the character parameter." Journal of Economics and Administrative Sciences 15, no. 53 (March 1, 2009): 1. http://dx.doi.org/10.33095/jeas.v15i53.1204.

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In this paper the method of singular value decomposition is used to estimate the ridge parameter of ridge regression estimator which is an alternative to ordinary least squares estimator when the general linear regression model suffer from near multicollinearity.

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McArdle, B. H. "The structural relationship: regression in biology." Canadian Journal of Zoology 66, no. 11 (November 1, 1988): 2329–39. http://dx.doi.org/10.1139/z88-348.

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Most biologists are now aware that ordinary least square regression is not appropriate when the X and Y variables are both subject to random error. When there is no information about their error variances, there is no correct unbiased solution. Although the major axis and reduced major axis (geometric mean) methods are widely recommended for this situation, they make different, equally restrictive assumptions about the error variances. By using simulated data sets that violate these assumptions, the reduced major axis method is shown to be generally more efficient and less biased than the major axis method. It is concluded that if the error rate of the X variable is thought to be more than a third of that on the Y variable, then the reduced major axis method is preferable; otherwise the least squares technique is acceptable. An analogous technique, the standard minor axis method, is described for use in place of least squares multiple regression when all of the variables are subject to error.

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Ahmed Issa, Mohamed Khalifa. "New Estimator for AR (1) Model with Missing Observations." Journal of University of Shanghai for Science and Technology 23, no. 09 (September 6, 2021): 147–59. http://dx.doi.org/10.51201/jusst/21/09521.

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In this paper, new form of the parameters of AR(1) with constant term with missing observations has been derived by using Ordinary Least Squares (OLS) method, Also, the properties of OLS estimator are discussed, moreover, an extension of Youssef [18]has been suggested for AR(1) with constant with missing observations. A comparative study between (OLS), Yule-Walker (YW) and modification of the ordinary least squares (MOLS) is considered in the case of stationary and near unit root time series, using Monte Carlo simulation.

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