Shrinkage estimation under multivariate elliptic models

Arashi, M. and Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X and Tabatabaey, S. M. M. and Soleimani, H. (2013) Shrinkage estimation under multivariate elliptic models. Communications in Statistics - Theory and Methods, 42 (11). pp. 2084-2103. ISSN 0361-0926


Abstract

The estimation of the location vector of a p-variate elliptically contoured distribution (ECD) is considered using independent random samples from two multivariate
elliptically contoured populations when it is apriori suspected that the location vectors of the two populations are equal. For the setting where the covariance structure of the populations is the same, we define the maximum likelihood, Stein-type shrinkage and positive-rule shrinkage estimators. The exact expressions for the bias and quadratic risk functions of the estimators are derived. The comparison of the quadratic risk functions reveals the dominance of the Stein-type estimators if p ≥ 3. A graphical illustration of the risk functions under a 'typical' member of the elliptically contoured family of distributions is provided to confirm the analytical results.


Statistics for USQ ePrint 23493
Statistics for this ePrint Item
Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version made not accessible.
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: 17 May 2013 06:14
Last Modified: 02 May 2017 23:49
Uncontrolled Keywords: bias; risk functions; elliptically contoured distributions; Hotteling's T2 statistic; quadratic loss; Stein-type and positive-rule shrinkage estimators.
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
14 Economics > 1403 Econometrics > 140304 Panel Data Analysis
01 Mathematical Sciences > 0102 Applied Mathematics > 010203 Calculus of Variations, Systems Theory and Control Theory
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490509 Statistical theory
38 ECONOMICS > 3802 Econometrics > 380204 Panel data analysis
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
Identification Number or DOI: https://doi.org/10.1080/03610926.2011.602492
URI: http://eprints.usq.edu.au/id/eprint/23493

Actions (login required)

View Item Archive Repository Staff Only