Robust M Hybrid Estimation in Linear Regression Model Based on PCA – Ridge Estimator

Two common data anomalies that significantly impair the performance of traditional regression estimators are multicollinearity and outliers in the predictor space. While a number of shrinkage and robust estimation strategies have been proposed separately, there is no much focus on creating estimators that can concurrently solve both issues inside a single framework. This study proposes a novel Robust M Principal Component – Ridge estimation approach that integrates robust M – estimation, principal component analysis (PCA) and ridge regression to enhance parameter estimation in contaminated regression models. Theoretical properties of the proposed estimator were derived through mean square error (MSE) analysis and compared with existing robust ridge, Liu, PCA and PCA – ridge estimators. A comprehensive Monte Carlo simulation experiment involving varying sample sizes, error variances, multicollinearity levels and 10% contamination (outliers) in the predictor space was conducted. Results indicate that the proposed estimators consistently achieved lower MSE values than competing estimators across most experimental settings. In particular, the MPCACK2MIN estimator emerged as the most efficient estimator, followed by MPCACK1 and MPCACK2. The proposed methodology provides a reliable alternative for regression modelling in the presence of simultaneous multicollinearity and predictor – space outliers.