[公告] 演講公告 (與上篇有關)
國立交通大學、清華大學 統計學研究所 專題演講
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07日(星期二)下午13:30-16:30
(下午13：00-13：30茶會於統計所428室舉行)
地 點：交大綜合一館427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.
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