Modified Ridge Regression With Cook’s Distance for Semiparametric Regression Models

Najeeb Mahmood Khan, Muhammad Aman Ullah, Javaria Ahmad Khan, Salman Raza and Nian-Sheng Tang

Journal of Mathematics, 2025, vol. 2025, 1-13

Abstract: Multicollinearity and influential cases in semiparametric regression models lead to biased and unreliable estimates distorting leverage and residual patterns. To address these challenges, we propose modified penalized least squares estimators (MPLSEs). We use Cook’s distance and a case deletion approach to evaluate their performance. The effectiveness of MPLSEs is demonstrated through the Longley dataset, where Cook’s distance is applied to the estimated coefficients, fitted values, residuals, and leverages, using a modified ridge parameter. In addition, a Monte Carlo simulation examines the influence of Cook’s distance across varying levels of multicollinearity, influential observations, and sample sizes. We compare MPLSEs with penalized least squares estimators (PLSEs) to assess their relative performance. The results show that MPLSEs outperform existing methods, effectively managing multicollinearity even with influential points. Our study aims to propose and validate a robust approach for addressing the challenges of multicollinearity and influential observations in semiparametric regression models.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2025/3801827.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2025/3801827.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3801827

DOI: 10.1155/jom/3801827

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().