A revised Cholesky decomposition to combat multicollinearity in multiple regression models. Issue 12 (13th August 2017)

• Record Type: Journal Article
• Authors: Babaie-Kafaki, Saman; Roozbeh, Mahdi
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 12(2017)
• Page Start: 2298
• Page End: 2308
• Publication Date: 2017-08-13
• Subjects: Linear regression -- multicollinearity -- ordinary least-squares estimator -- ridge estimator -- Cholesky decomposition; Primary: 62J05 -- 65F10 -- Secondary: 62J07 -- 65F15; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2017.1328599
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: As known, the ordinary least-squares estimator (OLSE) is unbiased and also, has the minimum variance among all the linear unbiased estimators. However, under multicollinearity the estimator is generally unstable and poor in the sense that variance of the regression coefficients may be inflated and absolute values of the estimates may be too large. There are several classes of biased estimators in statistical literature to decrease the effect of multicollinearity in the design matrix. Here, based on the Cholesky decomposition, we propose such an estimator which makes the data to be slightly distorted. The exact risk expressions as well as the biases are derived for the proposed estimator. Also, some results demonstrating superiority of the suggested estimator over OLSE are obtained. Finally, a Monté-Carlo simulation study and a real data application related to acetylene data are presented to support our theoretical discussions.