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CONFLICT AMONG THE SHRINKAGE ESTIMATORS INDUCED BY W, LR AND LM TESTS UNDER A STUDENT'S t REGRESSION MODEL  

Kibria, B.M.-Golam (Department of Statistics, Florida International University)
Publication Information
Journal of the Korean Statistical Society / v.33, no.4, 2004 , pp. 411-433 More about this Journal
Abstract
The shrinkage preliminary test ridge regression estimators (SPTRRE) based on Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests for estimating the regression parameters of the multiple linear regression model with multivariate Student's t error distribution are considered in this paper. The quadratic biases and risks of the proposed estimators are compared under both null and alternative hypotheses. It is observed that there is conflict among the three estimators with respect to their risks because of certain inequalities that exist among the test statistics. In the neighborhood of the restriction, the SPTRRE based on LM test has the smallest risk followed by the estimators based on LR and W tests. However, the SPTRRE based on W test performs the best followed by the LR and LM based estimators when the parameters move away from the subspace of the restrictions. Some tables for the maximum and minimum guaranteed efficiency of the proposed estimators have been given, which allow us to determine the optimum level of significance corresponding to the optimum estimator among proposed estimators. It is evident that in the choice of the smallest significance level to yield the best estimator the SPTRRE based on Wald test dominates the other two estimators.
Keywords
Efficiency; Lagrangian multiplier; likelihood ratio test; ridge regression; risk; shrinkage estimation; Student's t; superiority; Wald test;
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