A robust counterpart approach for the ridge estimator to tackle outlier effect in restricted multicollinear regression models

Abstract

In statistics, regression analysis is a method for predicting a target variable by establishing the optimal linear relationship between the dependent and independent variables. The ordinary least squares estimator (OLSE) is the optimal estimation method in classical regression analysis based on the Gauss–Markov theorem if the essential assumptions of normality, independence of error terms, and little or no multicollinearity in the covariates are satisfied. OLSE is profoundly affected by the collinearity between explanatory variables and outlier problems. Therefore, we require resilient strategies to resolve these challenges. Robust stochastic ridge regression is an alternative optimization problem to least squares regression when data are simultaneously contaminated by anomalies, influential observations, and multicollinearity. To combat outliers and multicollinearity problems, a robust stochastic ridge regression estimator based on the least squares trimmed method is proposed in this paper. Using simulated and real data sets, the efficacy of the proposed method with correlated and uncorrelated errors is then evaluated.