A new estimator in multiple linear regression model

Article type: Research Article

Authors: Alheety, M.I.^{; *} | Gore, S.D.

Affiliations: Department of Statistics, Faculty of Science, Pune University, Pune, India

Correspondence: [*] Corresponding author. E-mail: alheety@yahoo.com.

Abstract: Least squares estimates of parameters of a multiple linear regression model are known to be highly variable when the matrix on independent variables has the multicollinearity problem. To circumvent this problem, several alternative methods have been suggested to improve the precision of estimators. In this paper, we introduce a new type of biased estimate so-called Al estimator to reduce the effect of multicollinearity on the estimators. By some theorems and a simulation study, we show that, this new estimator has desirable properties as the ordinary ridge estimator and it is better than the ordinary least squares estimator and Liu estimator in terms of the matrix of mean square error. A numerical example from literature is used to illustrate the results.

Keywords: Al estimator, least squares estimator, Liu estimator, mean square error matrix, multicollinearity, ordinary ridge estimator

DOI: 10.3233/MAS-2008-3303

Journal: Model Assisted Statistics and Applications, vol. 3, no. 3, pp. 187-200, 2008