WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
The Performance of Robust Latent Root Regression Based on MM and Modified GM Estimators
Authors: ,
Abstract: It is now evident that the Ordinary Least Squares (OLS) estimator suffers a huge set back in the presence of multicollinearity. As an alternative, the Latent Root Regression (LRR) is put forward to remedy this problem. Nevertheless, it is now evident that the LRR performs poorly when outliers exist in a data. In this paper, we propose an improved version of the LRR to rectify the problem of multicollinearity which comes together with the existence of outliers. The proposed method is formulated by incorporating robust MM - estimator and modified generalized M- estimator (MGM) in the LRR algorithm. We call these methods the Latent Root MM-based (LRMMB) and the Latent Root MGM-based (LRMGMB) methods. The performance of our developed methods are compared with some existing methods such as the OLS, LRR, and the Latent Root M-based (LRMB). The numerical results indicate that the LRR performs very well in the presence of multicollinearity, but performs poorly in the presence of outliers. The proposed methods (LRMMB and LRMGMB) are more efficient than the OLS and the LRR estimators for data having both problems of multicollinearity and outliers.
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Pages: 916-924
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #89