交 通 大 學 統 計 學 研 究 所 專 題 研 討 會 題 目: Data Depth: Multivariate Ordering, Spacings, Nonparametric Statistics, and Its Far Ranging Applications 主講人: Prof. Regina Liu (劉月琴教授) Department of Statistics & Biostatistics Rugers, the State University of New Jersey, USA 時 間: 97年10月7日（星期二）13：30 - 16：30 （下午13：00-13：30茶會於統計所428室舉行） 地 點: 綜合一館427研討室 Abstract The advances in computer technology have facilitated greatly the collection of massive high dimensional data, and statisticians face increasingly the task of analyzing large multivariate datasets. The classical multivariate analysis is well developed, but its applicability is often limited to elliptical distributions. Data depth provides a powerful alternative. We develop the systematic nonparametric multivariate analysis using data depth, from distributional characterizations to inference. We also discuss how data depth gives rise to multivariate ordering and spacings, which have surprisingly far reaching applications. As an example, we introduce and develop multivariate spacings using the order statistics derived from data depth. Specifically, the spacing between two consecutive order statistics is the region which bridges the two order statistics, in the sense that the region contains all the points whose depth values fall between the depth values of the two consecutive order statistics. These multivariate spacings can be viewed as a data-driven realization of the so-called "statistically equivalent blocks". These spacings assume a form of center-outward layers of "shells" ("rings" in the two-dimensional case), for which the shapes of the shells follow closely the underlying probabilistic geometry. We discuss the properties and applications of these spacings. For example, we use the spacings to construct tolerance regions. The construction is nonparametric and completely data driven, and the resulting tolerance region reflects the true geometry of the underlying distribution. This is different from the existing approaches which require that the shape of the tolerance region be specified in advance. Finally, we also discuss several families of multivariate goodness-of-fit tests based on the proposed spacings. 敬請公佈 歡迎參加 --

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