A Unified Approach to Non-minimaxity of Sets of Linear Combinations of Restricted Location Estimators

Tatsuya Kubokawa and William E. Strawderman
Additional contact information
Tatsuya Kubokawa: Faculty of Economics, University of Tokyo
William E. Strawderman: Department of Statistics, Rutgers University

No CIRJE-F-786, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper studies minimaxity of estimators of a set of linear combinations of location parameters μi, i = 1, . . . , k under quadratic loss. When each location parameter is known to be positive, previous results about minimaxity or non-minimaxity are extended from the case of estimating a single linear combination, to estimating any number of linear combinations. Necessary and/or sufficient conditions for minimaxity of general estimators are derived. Particular attention is paid to the generalized Bayes estimator with respect to the uniform distribution and to the truncated version of the unbiased estimator (which is the maximum likelihood estimator for symmetric unimodal distributions). A necessary and sufficient condition for minimaxity of the uniform prior generalized Bayes estimator is particularly simple; If one estimates µ = A¹ where A is an ℓ × k known matrix, the estimator is minimax if and only if (AAt)ij ≤ 0 for any i and j, (i ̸= j). This condition is also sufficient (but not necessary) for minimaxity of the MLE.

Pages: 26pages
Date: 2011-01
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2011/2011cf786.pdf (application/pdf)

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:tky:fseres:2011cf786

Access Statistics for this paper

More papers in CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by CIRJE administrative office ().