Weighted robust improved KL M-estimators for linear regression model in presence of multicollinearity and outliers: simulation and applications

In the presence of multicollinearity and outliers, the ordinary least squares (OLS) estimator becomes unstable. In addition, existing ridge and robust ridge estimators tend to become ineffective when there is significant contamination. This paper presents a novel class of weighted robust improved Kibria–Lukman ridge M-estimators that expand existing robust ridge estimators by combining robust weighting methods along with improved shrinkage structures. The suggested estimators are built utilizing composite shrinkage functions based on harmonic, geometric, minimum, and product-based combinations, which are further modified by robust weight functions, in contrast to the current Kibria–Lukman (KL) and robust ridge M-estimators. This formulation improves resilience and stability in the presence of both multicollinearity and y-directional outliers. A real-data application and extensive Monte Carlo simulations under various multicollinearity levels, sample sizes, error variances, outlier proportions, and heavy-tailed error distributions are used to assess their performance. The findings demonstrate that, especially in situations with strong multicollinearity and significant outlier contamination, the suggested estimators particularly SQD2 and SQD4, consistently yield lower mean squared error (MSE) than competing estimators. Significantly, SQD4 achieved up to 80% lower MSE than Kibria Lukman M-estimators under high multicollinearity and 20% contamination.