Modified Ridge Regression With Cook’s Distance for Semiparametric Regression Models

Multicollinearity and influential cases in semiparametric regression models lead to biased and unreliable estimates distorting leverage and residual patterns. To address these challenges, we propose modified penalized least squares estimators (MPLSEs). We use Cook’s distance and a case deletion approach to evaluate their performance. The effectiveness of MPLSEs is demonstrated through the Longley dataset, where Cook’s distance is applied to the estimated coefficients, fitted values, residuals, and leverages, using a modified ridge parameter. In addition, a Monte Carlo simulation examines the influence of Cook’s distance across varying levels of multicollinearity, influential observations, and sample sizes. We compare MPLSEs with penalized least squares estimators (PLSEs) to assess their relative performance. The results show that MPLSEs outperform existing methods, effectively managing multicollinearity even with influential points. Our study aims to propose and validate a robust approach for addressing the challenges of multicollinearity and influential observations in semiparametric regression models.