Principal Component Preliminary Test Estimator in the Linear Regression Model

Abstract

A Preliminary Test Estimator is introduced based on Principal Component Regression Estimator defined in the linear regression model when the stochastic restrictions are available in addition to the sample information, and when the explanatory variables are multicollinear. It is further developed as a large sample preliminary test estimator by using Wald (WA), Likelihood Ratio (LR), and Lagrangian Multiplier (LM) tests. Stochastic properties of this estimator based on F test as well as WA, LR, and LM tests are derived, and the performance of the estimator is compared using WA, LR, and LM tests with respect to Mean Square Error Matrix (MSEM). A Monte Carlo simulation is carried out to illustrate the theoretical findings.