期刊名称：International Journal of Statistics and Probability
印刷版ISSN：1927-7032
电子版ISSN：1927-7040
出版年度：2017
卷号：6
期号：6
页码：24
DOI：10.5539/ijsp.v6n6p24
出版社：Canadian Center of Science and Education
摘要：Given Gaussian observation vectors $[\seqcl{\BY}{n}]$ having a common mean and dispersion matrix, a pervading issue is to identify shifted observations of type $\{\BYi\!\to\!\BYi\!+\!\bdeli\}.$ Conventional usage enjoins Hotelling's $\Tisq$ diagnostics, derived and applied under the mutual independence of $[\seqcl{\BY}{n}]$. Independence often fails, yet the need to identify outliers nonetheless persists. Accordingly, the present study reexamines $\Tisq$ under dependencies to include equicorrelations and more general matrices. Such dependencies are found in the analysis of calibrated vector measurements and elsewhere. In addition, mixtures of these distributions having star--shaped contours arise on occasion in practice. Nonetheless, the $\Tisq$ diagnostics are shown to remain exact in level and power for all such mixtures. Moreover, further matrix distributions, not necessarily having finite moments, are seen to generalize $n$--dimensional spherical symmetry to include non--Gaussian matrices of order $(n\!\times\!k)$ supporting $\Tisq.$ For these the use of $\Tisq$ remains exact in level. These findings serve to expand considerably the range of applicability of $\Tisq$ in practice, to include matrix Cauchy and other heavy tailed distributions intrinsic to econometric and other studies. Case studies serve to illuminate the methodology.
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