Bootstrap-quantile ridge estimator for linear regression with applications

Abstract

Bootstrap is a simple, yet powerful method of estimation based on the concept of random sampling with replacement. The ridge regression using a biasing parameter has become a viable alternative to the ordinary least square regression model for the analysis of data where predictors are collinear. This paper develops a nonparametric bootstrap-quantile approach for the estimation of ridge parameter in the linear regression model. The proposed method is illustrated using some popular and widely used ridge estimators, but this idea can be extended to any ridge estimator. Monte Carlo simulations are carried out to compare the performance of the proposed estimators with their baseline counterparts. It is demonstrated empirically that MSE obtained from our suggested bootstrap-quantile approach are substantially smaller than their baseline estimators especially when collinearity is high. Application to real data sets reveals the suitability of the idea.