Minimaxity of the Stein risk-minimization estimator for a normal mean matrix

Kubokawa Tatsuya and Tsukuma Hisayuki
Additional contact information
Tsukuma Hisayuki: Toho University, Faculty of Medicine, Tokyo 143-8540, Japan

Statistics & Risk Modeling, 2009, vol. 26, issue 4, 243-261

Abstract: This paper addresses the Stein conjecture in the simultaneous estimation of a matrix mean of a multivariate normal distribution with a known covariance matrix. Stein (1973) derived an unbiased estimator of a risk function for orthogonally equivariant estimators and considered to isotonize the estimator which minimizes the main part of the unbiased risk-estimator. We call it the Stein risk-minimization estimator (RM) in this paper. Although the Stein RM estimator has been recognized as an excellent procedure with a nice risk-performance, it has a complicated form based on the isotonizing algorithm, and no analytical properties such as minimaxity have been shown. The aim of this paper is to fix this conjecture in lower dimensional cases, that is, the minimaxity of the Stein RM estimator is established for the two and three dimensions.

Keywords: Decision theory; isotonic regression; Stein estimator; minimaxity; quadratic loss (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1524/stnd.2008.1011 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:26:y:2009:i:4:p:243-261:n:2

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1524/stnd.2008.1011

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().