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.