Some Influential Diagnostics in New Two-Parameter Estimator in the presence of multicollinearity and extreme values: Simulations and Applications

Abstract

Identifying influential points in linear regression is vital for ensuring the validity of inferential conclusions. Traditional diagnostic measures, such as DFFITs (DFT), Cook’s D (CKD), COVRATIO (CVR), Hadi’s measure (HAD), Pena’s statistic (PEN), and Atkinson statistic (ATK), are typically based on the Ordinary Least Squares (OLS) estimator, which assumes no violation of the basic linear regression assumptions. This study develops new diagnostic measures for these statistics using the New Two-Parameter (NTP) estimator to address multicollinearity. The study evaluated the performance of these measures through simulation studies with 1,000 replications under varying levels of multicollinearity, error variances, outlier percentages and magnitudes, and sample sizes. Results revealed that the newly proposed CVR measure with the NTP estimator achieved 100% detection of influential points and recorded the highest detection counts, outperforming all other measures. While traditional measures like CKD, PEN, and ATK based on OLS were effective only for small sample sizes in the absence of multicollinearity, their performance declined when multicollinearity was present. Conversely, CVRNTP consistently demonstrated superior performance when multicollinearity was mitigated. These findings suggest that the proposed CVRNTP is a robust tool for identifying influential points in datasets affected by multicollinearity. Real-life data applications further validated their performances.