Correlation Based Ridge Parameters in Ridge Regression with Heteroscedastic Errors and Outliers

A.V Dorugade

doi:10.2991/jsta.2015.14.4.6

Abstract

This paper introduces some new estimators for estimating ridge parameter, based on correlation between response and regressor variables for ridge regression analysis. A simulation study has been made to evaluate the performance of proposed estimators based on the minimum mean squared error (MSE) criterion compared to ordinary least squares (LS) estimator and ordinary ridge regression (RR) estimator. The simulation studies demonstrated that the suggested estimators are superior to LS and RR estimators in ridge regression analysis with Heteroscedastic and/or correlated errors, outlier observations.

Highlights

The multiple regression model is the most widely used statistical tool applied in all most every discipline, estimation of unknown parameters is a common interest for many users
In the present literature related to ridge parameter most of the researchers compare superiority of their suggested estimators with other existing methods using well ridge estimator given by Hoerl and Kennard (1970) in terms of minimum mean squared error (MSE) criterion
Case (d): In this case we evaluate the performance of proposed estimators for the simulated data exits with outliers and Heteroscedastic and/or correlated errors, in linear regression model in the presence of multicollinearity

Summary

Introduction

The multiple regression model is the most widely used statistical tool applied in all most every discipline, estimation of unknown parameters is a common interest for many users. The Ridge Regression (RR) estimator proposed by Hoerl and Kennard (1970) is the most popular biased estimator. In the present literature related to ridge parameter most of the researchers compare superiority of their suggested estimators with other existing methods using well ridge estimator given by Hoerl and Kennard (1970) in terms of minimum MSE criterion. In the present work we evaluate the performances of our suggested estimators of k using parameter estimation method given by Hoerl and Kennard (1970) in the presence of multicollinearity, outliers and Heteroscedastic random errors respectively.

Model and Estimators

Proposed Estimators

Comparison Between the α and α RR

Simulation Study

Conclusion

Methods