A new robust ridge parameter estimator having no outlier and ensuring normality for linear regression model

Abstract

In order to accurately estimate the regression coefficients in a multiple linear regression model having multicollinearity, ridge regression is a well-liked biased estimation technique used as an alternative to the least squares method. So far, numerous estimators have been proposed for ridge parameter estimation in the ridge regression method. In this study, a robust ridge parameter estimator that performs better than the 366 different ridge parameter estimators proposed in the literature to date has been developed using the "search method". In contrast to the studies in the literature, in addition to the Mean Square Error (MSE) criterion both the estimators and the developed robust ridge parameter estimator have been assessed in terms of outliers and normality. Furthermore, a simulation design with a total of 6050 cases were included in the study which corresponds to parameter values that varied widely in terms of the number of independent variables (p), sample size (n), correlation coefficient between independent variables (ρ), and standard deviation of errors (σ). Significant inter linear associations among the MSE, outlier detection and normality criteria were found. Results from the conducted simulation study revealed that the proposed robust ridge parameter estimator was the most effective one in terms of these three criteria, regardless of the number of regressors, sample size, multicollinearity level, and standard deviation of errors.