Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 3, pp. 311--320

TEST OF HOMOGENEITY OF VARIANCES AGAINST ORDERED ALTERNATIVES IN FIXED EFFECTS LINEAR MODELS

By

CAROL LYNNE HOFERKAMP, Truman State University, Kirksville

and

SHYAMAL DAS PEDDADA, National Institute of Environmental Health Sciences, RTP

SUMMARY. In this article we study the problem of testing for equality of variances of k independent normal linear models, with a common regression parameter, against ordered alternatives. As a uniformly most powerful invariant test may not exist even for the case where k = 2, a locally best invariant test is derived. Although such tests are proven not to exist when k>=3, we propose a test procedure which, under certain conditions on the design matrices, will be unbiased.

AMS (2000) subject classification. 62F30, 62F03, 62J05.

Key words and phrases. Homoscedasticity, locally best invariant tests, ordered alternatives, simple order restriction, unbiased tests.

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