On the size corrected tests in improved estimation

Hoque, Zahirul and Billah, Baki and Khan, Shahjahan (2005) On the size corrected tests in improved estimation. Calcutta Statistical Association Bulletin, 57 (227-22). pp. 143-160. ISSN 0008-0683

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Abstract

In this paper we propose shrinkage preliminary test estimator (SPTE) of the coefficient vector in the multiple linear regression model based on the size corrected Wald (W), likelihood ratio (LR) and Lagrangian multiplier (LM) tests. The correction factors used are those obtained from degrees of freedom corrections to the estimate of the error variance and those obtained from the second-order Edgeworth approximations to the exact distributions of the test statistics. The bias and weighted mean squared error (WMSE) functions of the estimators are derived. With respect to WMSE, the relative efficiencies of the SPTEs relative to the maximum likelihood estimator are calculated. This study shows that the amount of conflict can be substantial when the three tests are based on the same asymptotic chi-square critical value. The conflict among the SPTEs is due to the asymptotic tests not having the correct significance level. The Edgeworth size corrected W, LR and LM tests reduce the conflict remarkably.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Full citation: Hoque, Z., Billah, B. and Khan, S. (2005). On the Size Corrected Tests in Improved Estimation. Calcutta Statistical Association Bulletin, Vol 57 (127-128), 143-160.
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:37
Last Modified: 02 Jul 2013 22:36
Uncontrolled Keywords: Shrinkage preliminary test estimator; Wald, likelihood ratio and Lagrangian multiplier tests; bias and quadratic bias; %weighted mean squared error; relative efficiency; and conflicts.
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010401 Applied Statistics
URI: http://eprints.usq.edu.au/id/eprint/1238

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