Modified Almost Unbiased Liu Estimator in Linear Regression Model

Abstract

In this paper, we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator (AULE) and ridge estimator (RE) in a linear regression model when multicollinearity presents among the independent variables. Necessary and sufficient conditions for the proposed estimator over the ordinary least square estimator, RE, AULE and Liu estimator (LE) in the mean squared error matrix sense are derived, and the optimal biasing parameters are obtained. To illustrate the theoretical findings, a Monte Carlo simulation study is carried out and a numerical example is used.

Keywords

Multicollinearity / Ridge estimator / Almost unbiased Liu estimator / Liu estimator / Modified almost unbiased Liu estimator / Mean squared error matrix

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