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Journal of Probability and Statistics
Volume 2017, Article ID 2170816, 8 pages
https://doi.org/10.1155/2017/2170816
Research Article

Robust Group Identification and Variable Selection in Regression

Department of Statistics, College of Administration and Economics, University of Al-Qadisiyah, Al Diwaniyah, Iraq

Correspondence should be addressed to Ali Alkenani; qi.ude.uq@inanekla.ila

Received 16 September 2017; Accepted 3 December 2017; Published 20 December 2017

Academic Editor: Aera Thavaneswaran

Copyright © 2017 Ali Alkenani and Tahir R. Dikheel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The elimination of insignificant predictors and the combination of predictors with indistinguishable coefficients are the two issues raised in searching for the true model. Pairwise Absolute Clustering and Sparsity (PACS) achieves both goals. Unfortunately, PACS is sensitive to outliers due to its dependency on the least-squares loss function which is known to be very sensitive to unusual data. In this article, the sensitivity of PACS to outliers has been studied. Robust versions of PACS (RPACS) have been proposed by replacing the least squares and nonrobust weights in PACS with MM-estimation and robust weights depending on robust correlations instead of person correlation, respectively. A simulation study and two real data applications have been used to assess the effectiveness of the proposed methods.