A new general method for constructing confidence sets in arbitrary dimensions: with applications

DasGupta, A. ; Ghosh, J. K. ; Zen, M. M. (1995) A new general method for constructing confidence sets in arbitrary dimensions: with applications Annals of Statistics, 23 (4). pp. 1408-1432. ISSN 0090-5364

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Official URL: http://www.jstor.org/pss/2242771

Abstract

Let X have a star unimodal distribution P0 on Rp. We describe a general method for constructing a star-shaped set S with the property P0(X ∈ S) ≥ 1 - α, where 0 < α < 1 is fixed. This is done by using the Camp-Meidell inequality on the Minkowski functional of an arbitrary star-shaped set S and then minimizing Lebesgue measure in order to obtain size-efficient sets. Conditions are obtained under which this method reproduces a level (high density) set. The general theory is then applied to two specific examples: set estimation of a multivariate normal mean using a multivariate t prior and classical invariant estimation of a location vector θ for a mixture model. In the Bayesian example, a number of shape properties of the posterior distribution are established in the process. These results are of independent interest as well. A computer code is available from the authors for automated application. The methods presented here permit construction of explicit confidence sets under very limited assumptions when the underlying distributions are calculationally too complex to obtain level sets.

Item Type:Article
Source:Copyright of this article belongs to Institute of Mathematical Statistics.
ID Code:22555
Deposited On:24 Nov 2010 08:19
Last Modified:17 May 2016 06:34

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