Robust Regression Methods: Achieving Small Standard Errors When There Is Heteroscedasticity

2004 ◽  
Vol 3 (4) ◽  
pp. 349-364 ◽  
Author(s):  
Rand R. Wilcox ◽  
H. J. Keselman
Keyword(s):  
Robust Regression ◽  
Standard Errors ◽  
Regression Methods

scholarly journals Performances of LAD Regression, M-Regression and Quantile Regression Methods in order to Investigate Stock Prices of the Banks in the BIST Bank Index

2018 ◽  
Vol 6 (04) ◽  
Author(s):  
Umran Munire Kahraman ◽  
Neslihan Iyit
Keyword(s):  
Quantile Regression ◽  
Stock Prices ◽  
Robust Regression ◽  
Mean Squared Error ◽  
Stock Exchange ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Regression Methods ◽  
Istanbul Stock Exchange ◽  
Error Terms

In this study, performances of LAD regression, M-regression, Q25 and Q75 quantile regression models as robust regression methods alternative to the classical LS method are compared in the case of violations from the normality assumption of the error terms and the presence of an outlier. By using these alternative regression methods, stock prices of the 12 commercial banks and 1 participation bank listed in the Istanbul Stock Exchange (BIST) bank index between 2012 and 2016 are investigated in terms of equity size and equity profitability. As a result of this study, M-regression is the most suitable robust regression model with the smallest value of the mean squared error (MSE) measure and the small values for the standard errors of the parameter estimates belonging to the equity size and equity profitability. The smaller the standard errors of the parameter estimates, the narrower the resulting confidence intervals are obtained in M- regression. The accuracy as a measure of closeness of parameter estimates to the true values of the parameters is also obtained higher in M-regression.

On the use of robust regression methods in wind speed assessment

2016 ◽  
Vol 99 ◽  
pp. 1287-1298 ◽  
Author(s):  
Takvor H. Soukissian ◽  
Flora E. Karathanasi
Keyword(s):  
Wind Speed ◽  
Robust Regression ◽  
Regression Methods

Robust regression methods for computer vision: A review

1991 ◽  
Vol 6 (1) ◽  
pp. 59-70 ◽  
Author(s):  
Peter Meer ◽  
Doron Mintz ◽  
Azriel Rosenfeld ◽  
Dong Yoon Kim
Keyword(s):  
Computer Vision ◽  
Robust Regression ◽  
Regression Methods

Comments on a Note on Permutation Tests of Significance for Multiple Regression Coefficients by Long, et al.

2007 ◽  
Vol 101 (3_suppl) ◽  
pp. 1041-1042
Author(s):  
Bryan F. J. Manly
Keyword(s):  
Multiple Regression ◽  
Permutation Tests ◽  
Regression Coefficients ◽  
Standard Theory ◽  
Standard Errors ◽  
P Value ◽  
Randomization Tests ◽  
P Values ◽  
Regression Methods ◽  
Classical Regression

It is noted that a recent paper in the Journal may give a misleading impression of the robustness of classical regression methods. First, the authors show that p-values based on the randomization distributions of regression coefficients may be quite different from p-values based on t-distributions. However, there is no reason why these two types of p-value should be exactly the same, and p-values based on the randomization distributions of t-statistics are usually similar to p-values obtained from t-distributions. These latter p-values are perfectly valid for the purposes of randomization tests. Second, the authors imply that estimating the standard errors of regression coefficients by randomizing the order of the Y values gives better estimates of standard errors than standard theory. In fact these standard errors based on randomization will tend to be too large unless the regression equation accounts for none of the variation in the Y values.

scholarly journals Analysis of Efficiency of Least Trimmed Square and Least Median Square Methods in The Estimation of Robust Regression Parameters

2020 ◽  
Vol 4 (1) ◽  
pp. 21
Author(s):  
Hamdan Abdi ◽  
Sajaratud Dur ◽  
Rina Widyasar ◽  
Ismail Husein
Keyword(s):  
Observational Data ◽  
Palm Oil ◽  
Regression Models ◽  
Robust Regression ◽  
Least Squares Method ◽  
Regression Method ◽  
Estimation Methods ◽  
Land Area ◽  
Regression Methods ◽  
Regression Parameters

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

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