M—estimators based repeated significance tests for one—way anova with adaptation to multiple comparisons

Abstract

A repeated significance testing procedure for a multi—sample location problem based on a general class of M—estimators is considered. The asymptotic distribution theory of the allied test statistics is developed under the null hypothesis as well as under local alternatives. The theory is then adapted to provide a multiple comparison procedure which generalizes the classical Scheffé method to a pseudo—sequential setup. Allied asymptotic relative efficienty results are also considered.

Keywords:

• Asymptotic distribution
• asymptotic relative efficienty
• Bessel process
• multiple comparisons
• repeated significance testing
• Scheffé method