The Heteroscedastic Method II: Simplified Sampling

SYNOPTIC ABSTRACT

The multivariate Heteroscedastic Method was formulated to allow inferences with controlled statistical characteristics (such as controlled power for a test in addition to controlled level) in situations where the covariance matrices are unknown and (possibly) unequal (and do not have a known structure); this is the most common setting in practical applications. The method was formulated in a general form in 1979, and had already been (and has since been) extensively applied to the univariate case, solving such problems as that of Behrens-Fisher. In the multivariate case, application awaited an algorithm for construction of certain matrices needed in the method (which were known to exist, but for which a construction had not been given); algorithms appeared in 1987. In this paper we present a modification of the Heteroscedastic Method which allows the same exact control of characteristics of statistical procedures, but in a simplified setting: it does not need the cited matrices.

Key Words and Phrases:

• Heteroscedastic Method
• multivariate statistics
• simplified sampling
• statistical decision rules
• multivariate confidence regions
• asymptotic efficiency