New penalized M-estimators in robust ridge regression: real life applications using sports and tobacco data

Abstract

The ordinary least square and ridge regression estimators are very sensitive to the joint presence of multicollinearity and outliers in the y-direction. The method of robust ridge regression with penalized or biasing parameter provides biased but efficient results than least square and ridge regression estimators. The optimal choice of k m plays a key role in such a bias-variance tradeoff. In this paper, we have considered some existing estimators and also proposed some new penalized m-estimators. The new estimators have been compared with existing estimators through extensive Monte Carlo simulations. Based on the mean squared error criterion, the new penalized m-estimators outperform all the competing estimators under certain conditions. The Tobacco and Sports data sets have been used as numerical examples in the study. The findings show that the new penalized m-estimators outperform in the existing m-estimators.