Second-Order Properties of a Two-Stage Fixed-Size Confidence Region for the Mean Vector of a Multivariate Normal Distribution

N. Mukhopadhyay

Journal of Multivariate Analysis, 1999, vol. 68, issue 2, 250-263

Abstract: We consider the classical fixed-size confidence region estimation problem for the mean vector[mu]in theNp([mu], [Sigma]) population where [Sigma] is unknown but positive definite. We write[lambda]1for the largest characteristic root of [Sigma] and assume that[lambda]1is simple. Moreover, we suppose that, in many practical applications, we will often have available a number[lambda]*(>0) and that we can assume[lambda]1>[lambda]*. Given this addi- tional, and yet very minimal, knowledge regarding[lambda]1, the two-stage procedure of Chatterjee (Calcutta Statist. Assoc. Bull.8(1959a), 121-148;9(1959b), 20-28;11(1962), 144-159) is revised appropriately. The highlight in this paper involves the verification ofsecond-order propertiesassociated with such revised two-stage estimation techniques, along with the maintenance of the nominal confidence coefficient.

Keywords: spherical; confidence; region; coverage; probability; average; sample; number; Wishart; matrix; largest; characteristic; root; Hotelling's; T2 (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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