Preliminary test estimators for the multivariate normal mean based on the modified W, LR and LM tests

Khan, S. ORCID: https://orcid.org/0000-0002-0446-086X and Hoque, Z. (2003) Preliminary test estimators for the multivariate normal mean based on the modified W, LR and LM tests. Journal of Statistical Research, 37 (1). pp. 43-55. ISSN 0256-422X

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Abstract

In this paper we consider the preliminary test estimators (PTEs) of the mean vector of multivariate normal distribution under the modified Wald, likelihood ratio, and Lagrange multiplier tests. The properties of the estimators have been investigated under some popular statistical criteria. It has been observed that with respect to the quadratic bias the Wald test based PTE performs better than
those based on the likelihood ratio and Lagrange multiplier tests. Whereas, with respect to the quadratic risk the Lagrange multiplier test based PTE performs better than those based on the likelihood ratio and Wald tests. The results of this study reveal that the use of the three modified tests in the formation of the PTEs significantly reduces the conflict among the PTEs as compared to the
estimators based on the three original tests in terms of both quadratic bias and risk properties.

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Item Type:	Article (Commonwealth Reporting Category C)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	No evidence of copyright restrictions.
Faculty/School / Institute/Centre:	Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited:	30 Nov 2007 11:47
Last Modified:	08 Dec 2015 00:58
Uncontrolled Keywords:	preliminary test estimator; Wald; likelihood ratio and Lagrange multiplier tests; quadratic bias; quadratic risk; relative efficiency and conflict ict.
Fields of Research (2008):	01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified 01 Mathematical Sciences > 0104 Statistics > 010404 Probability Theory 01 Mathematical Sciences > 0102 Applied Mathematics > 010203 Calculus of Variations, Systems Theory and Control Theory
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4905 Statistics > 490599 Statistics not elsewhere classified 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490506 Probability theory 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490103 Calculus of variations, mathematical aspects of systems theory and control theory
Socio-Economic Objectives (2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI:	http://eprints.usq.edu.au/id/eprint/14526

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