Locally minimax tests for a multinormal data problem |
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Authors: | S Dahel N Giri Y Lepage |
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Institution: | (1) Department of Mathematics, Collège militaire royal de Saint-Jean, JOJ 1R0 Richelain, Québec, Canada |
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Abstract: | LetX be ap-normal random vector with unknown mean and unknown covariance matrix and letX be partitioned asX=(X
(1)
,X
(2)
, ...,X
(r)
) whereX
(j) is a subvector of dimensionp
j such that
j=1
r
p
j
=p. We show that the tests, obtained by Dahel (1988), are locally minimax. These tests have been derived to confront Ho: =0 versusH
1: 0 on the basis of sample of sizeN, X
1, ..., XN, drawn fromX andr additional samples of sizeN
j, U
i
(j)
, i=1, ..., Nj, drawn fromX
(1), ...X
(r) respectively. We assume that the (r+1) samples are independent and thatN
j>p
j forj=0, 1, ..., r (N
oN andp
op). Whenr=2 andp=2, a Monte Carlo study is performed to compare these tests with the likelihood ratio test (LRT) given by Srivastava (1985). We also show that no locally most powerful invariant test exists for this problem. |
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Keywords: | |
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