The Multivariate Heteroscedastic Method: Distributions of Statistics and an Application

SYNOPTIC ABSTRACT

Asymptotic approximations to the distributions of the basic variate, and of some statistics constructed by the heteroscedastic method are derived for the multivariate case. The results are numerically compared with exact ones in the case of one and/or two dimensions. As an application, simultaneous confidence interval estimation with a given length, for the difference of two normal population mean vectors, is considered and a numerical example given using Fisher's iris data.

Key Words and Phrases:

• asymptotic expansions
• heteroscedastic method
• difference of mean vectors
• simultaneous confidence intervals
• two-stage sampling scheme