On a notion of simplicial depth.

Abstract:

:For a distribution F on R(p) and a point x in R(p) the simplicial depth D(x), which is the probability that x be inside a random simplex whose vertices are p + 1 independent observations from F, is introduced. D(x) can be viewed as a measure of depth of the point x relative to F, and its empirical version gives rise to a natural ordering of the data points from the center outward. This ordering provides an approach for detecting outliers in a multivariate data cloud and leads to the introduction of affine equivariant multivariate generalizations of the univariate sample median and L-statistics. This sample median is shown to be consistent for the center of any angularly symmetric distribution.

authors

Liu RY

doi

10.1073/pnas.85.6.1732

keywords:

subject

Has Abstract

pub_date

1988-03-01 00:00:00

pages

1732-4

issue

6

eissn

0027-8424

issn

1091-6490

journal_volume

85

pub_type

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