OPTIMAL TESTS FOR NO CONTAMINATION IN SYMMETRIC MULTIVARIATE NORMAL MIXTURES

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

1University of California, Santa Barbara, U.S.A. 2Computer 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, σ^{2}, are known. Here, we establish that even under the general situation, when some or none of m and σ^{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.