Robustness of testing procedures for Behrens-Fisher problem with normal mixture data.

摘要

The problem of comparing the mean values of two populations has a great importance in applied statistics. Such comparison consists of either testing the hypothesis that the difference between the two means is equal to a given value or constructing a confidence interval for their difference. If in addition, the two populations are heteroscedastic (i.e., have different variances), then the problem becomes what is known as "Behrens-Fisher problem " named after its first two investigators. Furthermore, non-normality in the data will add further complications in testing the hypothesis.;The first aim of this thesis is to give a comprehensive review of literature of the currently available strategies for both univariate and multivariate Behrens-Fisher problem and summarize the related Monte Carlo studies as reported in the literature. The second aim is to carry out additional Monte Carlo comparisons of some of these procedures in order to shed light on their robustness when applied to data from normal mixture distributions.