Robust multiple regression based on shrinkage $\mathbf{S}_{n}$ estimator

Lakshmi R; Sajesh T A

Article Details

Robust multiple regression based on shrinkage $\mathbf{S}_{n}$ estimator

Authors:

Lakshmi R | Sajesh T A

Publisher:

Hacettepe University

Main Topics:

Computational Statistics | Statistical Analysis | Applied Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 3, pp.1062-1093

Document Type:

Article

Publication Date:

6/2025

Document Language:

English

Document ID (Org No.):

2001351218

pISSN:

2651-477X

Keywords:

Abstract:

 Regression analysis is used to model the data statistically. However, data modeling and interpretation are affected by outliers and significant points. Robust regression analysis offers an alternative. In this study, the parameters that define the linear regression problem are estimated using a robust approach. The concept of shrinkage, which has been investigated for outlier detection in multivariate data. A comprehensive simulation analysis is performed to examine the breakdown value of the regression estimator, the affine equivariance, the robustness against contamination, and the efficiency with normal errors. The advantages of the suggested robust estimator in regression are demonstrated by the simulation results and real-world data examples. Simulation and research are conducted using the R software.

 Regression analysis is used to model the data statistically. However, data modeling and interpretation are affected by outliers and significant points. Robust regression analysis offers an alternative. In this study, the parameters that define the linear regression problem are estimated using a robust approach. The concept of shrinkage, which has been investigated for outlier detection in multivariate data. A comprehensive simulation analysis is performed to examine the breakdown value of the regression estimator, the affine equivariance, the robustness against contamination, and the efficiency with normal errors. The advantages of the suggested robust estimator in regression are demonstrated by the simulation results and real-world data examples. Simulation and research are conducted using the R software.

 Regression analysis is used to model the data statistically. However, data modeling and interpretation are affected by outliers and significant points. Robust regression analysis offers an alternative. In this study, the parameters that define the linear regression problem are estimated using a robust approach. The concept of shrinkage, which has been investigated for outlier detection in multivariate data. A comprehensive simulation analysis is performed to examine the breakdown value of the regression estimator, the affine equivariance, the robustness against contamination, and the efficiency with normal errors. The advantages of the suggested robust estimator in regression are demonstrated by the simulation results and real-world data examples. Simulation and research are conducted using the R software.

 Regression analysis is used to model the data statistically. However, data modeling and interpretation are affected by outliers and significant points. Robust regression analysis offers an alternative. In this study, the parameters that define the linear regression problem are estimated using a robust approach. The concept of shrinkage, which has been investigated for outlier detection in multivariate data. A comprehensive simulation analysis is performed to examine the breakdown value of the regression estimator, the affine equivariance, the robustness against contamination, and the efficiency with normal errors. The advantages of the suggested robust estimator in regression are demonstrated by the simulation results and real-world data examples. Simulation and research are conducted using the R software.

Article Details

Robust multiple regression based on shrinkage $\mathbf{S}_{n}$ estimator

Authors:

Lakshmi R | Sajesh T A

Publisher:

Hacettepe University

Main Topics:

Computational Statistics | Statistical Analysis | Applied Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 3, pp.1062-1093

Document Type:

Article

Publication Date:

6/2025

Document Language:

English

Document ID (Org No.):

2001351218

pISSN:

2651-477X

Data modeling

regression

reweighted estimator

robust shrinkage $S_{n}$

Issues

Article Details

Robust multiple regression based on shrinkage $\mathbf{S}_{n}$ estimator

Authors: Lakshmi R | Sajesh T A

Publisher: Hacettepe University

Main Topics: Computational Statistics | Statistical Analysis | Applied Statistics

Journal: Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 3, pp.1062-1093

Document Type: Article

Publication Date: 6/2025

Document Language: English

Document ID (Org No.): 2001351218

pISSN: 2651-477X

Data modeling

regression

reweighted estimator

robust shrinkage $S_{n}$

Issues

Authors:

Lakshmi R | Sajesh T A

Publisher:

Hacettepe University

Main Topics:

Computational Statistics | Statistical Analysis | Applied Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 3, pp.1062-1093

Document Type:

Article

Publication Date:

6/2025

Document Language:

English

Document ID (Org No.):

2001351218

pISSN:

2651-477X