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OPTIMAL TESTS FOR NO CONTAMINATION IN

SYMMETRIC MULTIVARIATE NORMAL MIXTURES

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ASHIS SENGUPTA^{1,2} AND CHANDRANATH PAL^{2}

^{1} *University of California, Santa Barbara, U.S.A.*

^{2} *Computer Science Unit, Indian Statistical Institute,*

203 Barrackpore Trunk Road, Calcutta 700 035, India
(Received April 11, 1990; revised January 6, 1992)

**Abstract.**
SenGupta and Pal (1991, *J. Statist. Plann.
Inference*, **29**, 145-155) have recently obtained the locally
optimal test for zero intraclass correlation coefficient in symmetric
multivariate normal mixtures, with known mixing proportion, for the case when
the common mean, *m*, and the common variance, *sigma*^{2}, are known. Here,
we establish that even under the general situation, when some or none of *m*
and *sigma*^{2} are known, simple optimal tests can be derived, which are
locally most powerful similar, whose exact cut-off points are already
available and which retain all the previous optimality properties, e.g.
unbiasedness, monotonicity and consistency. Some power tables are presented
to demonstrate the favorable performances of these tests.

*Key words and phrases*:
Intraclass correlation coefficient, locally
most powerful similar test, mixture distribution.

**Source**
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