On Liu's simplicial depth and Randles' interdirections

Multivariate Signed Ranks : Randles’ Interdirections or Tyler’s Angles?

Hallin and Paindaveine (2002a) developed, for the multivariate (elliptically symmetric) one-sample location problem, a class of optimal procedures, based on Randles’ interdirections and the ranks of pseudo-Mahalanobis distances. We present an alternative version of these procedures in which interdirections are replaced by “Tyler angles”, namely, the angles between the observations standardized ...

Optimal signed-rank tests based on hyperplanes

For analysing k-variate data sets, Randles (1989) considered hyperplanes going through k− 1 data points and the origin. He then introduced an empirical angular distance between two k-variate data vectors based on the number of hyperplanes (the so-called interdirections) that separate these two points, and proposed a multivariate sign test based on those interdirections. In this paper, we presen...

On Isomorphism of Simplicial Complexes and Their Related Algebras

Asymptotic Linearity of Serial and Nonserial Multivariate Signed Rank Statistics

Asymptotic linearity plays a key role in estimation and testing in the presence of nuisance parameters. This property is established, in the very general context of a multivariate general linear model with elliptical VARMA errors, for the serial and nonserial multivariate rank statistics considered in Hallin and Paindaveine (2002a and b, 2004a) and Oja and Paindaveine (2004). These statistics, ...

Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.