Generalized Cook’s Distance and DFFITs for the New Biased-Based Estimator in the Presence of Multicollinearity and Outliers

Abstract

Regression analysis is a powerful tool for modeling relationships between variables, but its reliability hinges on meeting key assumptions of the classical linear regression model. When multicollinearity and outliers are simultaneously present, traditional estimation techniques such as Ordinary Least Squares (OLS) become unreliable, and classical influence diagnostics like Cook’s Distance and DFFITs may fail to detect influential observations accurately. To address this gap, this study develops generalized versions of Cook’s Distance and DFFITs tailored to the New Biased-Based (NBB) estimator a two-parameter estimator designed to mitigate multicollinearity. Using case-deletion and approximate analytical approaches, we derive influence diagnostics that incorporate the structure of the NBB estimator. The proposed methods are then applied to economic and manufacturing datasets known to exhibit both multicollinearity and outliers. Results demonstrate that the new diagnostic measures, viz; Cook’s D in NBB (CD_NBB) and DFFITs in NBB (DF_NBB) are effective in identifying influential observations, showing strong alignment with and, in some cases, improvements over existing robust and biased diagnostic techniques. These findings suggest that the NBB-based influence diagnostics offer a valuable addition to the toolkit for regression analysis under complex data conditions.