On a notion of simplicial depth
AUTOR(ES)
Liu, Regina Y.
RESUMO
For a distribution F on Rp and a point x in Rp 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.
