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Data-dependent probability matching priors of the second order
Authors:S. H. Ong
Affiliation:Institute of Mathematical Sciences, University of Malaya , 50603, Kuala Lumpur, Malaysia
Abstract:In this paper, we consider the preliminary test approach for the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The preliminary test two-parameter estimators based on the Wald (W), likelihood ratio, and Lagrangian multiplier tests are given, when it is suspected that the regression parameter may be restricted to a subspace and the regression error is distributed with multivariate Student's t distribution. The bias and mean square error of the proposed estimators are derived and compared. The conditions of superiority of the proposed estimators are obtained. Finally, we conclude that the optimum choice of the level of significance becomes the traditional choice by using the Wald test.
Keywords:frequentist validity  Jeffreys’ prior  orthogonal parametrization  posterior quantile  shrinkage argument
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