EQUATIONS
Print ISSN: 2944-9146, E-ISSN: 2732-9976 An Open Access International Journal of Mathematical and Computational Methods in Science and Engineering
Volume 4, 2024
Some Influential Diagnostics in New Two-Parameter Estimator in the presence of multicollinearity and extreme values: Simulations and Applications
Authors: , , ,
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.
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Keywords: influential point, outliers, multicollinearity, Ordinary Least Squares, simulation studies
Pages: 91-110
DOI: 10.37394/232021.2024.4.11