科研成果详情

The outlier problem for a multivariate elliptically contoured distribution's random sample with mean slippage is defined and the likelihood ratio test ofthe null hypothesis, in which there are no outliers, versus the alternative hypothesis, in which some outliers are present, is derived. We show that the testing problemis invariant under a group of affine transformations and obtain the maximal in-variance which is equivalent to the likelihood ratio testing statistic. Furthermore, the non-null and null density distribution functions of the likelihood ratio testingstatistic are derived. We find that the null density distribution function of thetesting statistic is robust and the density distribution function is a monotonical likelihood ratio function of the maximal invariance. Therefore, the likelihood ratiotest is a uniformly most powerful invariant test among the group of affine transfor-mations. In the last section, we give an example of detecting multivariate outliersin elliptically contoured distribution.