Generalized Cross-Validation for Simultaneous Optimization of Tuning Parameters in Ridge Regression

Roozbeh, Mahdi and Arashi, M. and Hamzah, Nor Aishah (2020) Generalized Cross-Validation for Simultaneous Optimization of Tuning Parameters in Ridge Regression. Iranian Journal of Science and Technology, Transactions A: Science, 44 (2). pp. 473-485. ISSN 1028-6276, DOI

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When multicollinearity exists in the context of robust regression, ridge rank regression estimator can be used as an alternative to the rank estimator. Performance of the ridge rank regression estimator is highly dependent on the ridge parameter, here the tuning parameter. On the other hand, suppose we are provided with some non-sample uncertain prior information (UPI) about regression coefficients. Shrinkage estimation is a well-known strategy to improve estimation, under the UPI, where the amount of shrinkage is controlled by a tuning parameter. Hence, optimization of both tuning parameters can be a problem of interest. In this study, theoretical development of the generalized cross-validation (GCV) is considered and some numerical illustrations are given to validate the theoretical findings. Our results demonstrated that using the proposed GCV criterion, the shrinkage ridge rank regression estimator behaves well in the sense of minimum risk function. © 2020, Shiraz University.

Item Type: Article
Funders: Grant No. 97008633 from the Iran National Science Foundation (INSF), Grant Number 97019472 from the Iran National Science Foundation (INSF), National Research Foundation (NRF) of South Africa SARChI Research Chair UID: 71199 and Re: IFR170227223754 Grant No. 109214, Research Grant Support RP009B-13AFR from the University of Malaya
Uncontrolled Keywords: Generalized cross-validation; Multicollinearity; Rank regression; Ridge regression; Shrinkage
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms. Juhaida Abd Rahim
Date Deposited: 05 Aug 2020 02:05
Last Modified: 05 Aug 2020 02:05

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