Dept. Applied Statistics and Operations Research, Bowling Green State University, Bowling Green, Ohio 43403, USA.;Dept. Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403, USA.
Abstract:
The robustness of Mauchly's sphericity test criterion when sampling from a mixture of two multivariate normal distributions is studied. The distribution of the sphericity test criterion when the sample covariance matrix has a non-central Wishart density of rank one is derived in terms of Meijer's G-functions; its distribution under the mixture model is then deduced. The robustness is studied by computing actual significance levels of the test under the mixture model using the critical values under the usual normal model.