A Unified Approach to Non-minimaxity of Sets of Linear Combinations of Restricted Location Estimators
AbstractThis paper studies minimaxity of estimators of a set of linear combinations of location parameters Î¼i, 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 Âµ = AÂ¹ where A is an â„“ Ã— k known matrix, the estimator is minimax if and only if (AAt)ij â‰¤ 0 for any i and j, (i Ì¸= j). This condition is also sufficient (but not necessary) for minimaxity of the MLE.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-786.
Date of creation: Jan 2011
Date of revision:
Contact details of provider:
Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
More information through EDIRC
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office).
If references are entirely missing, you can add them using this form.