We tackle the classical two-sample spherical location problem for directional data by having recourse to the Le Cam methodology, habitually used in classical linear multivariate analysis. More precisely we construct locally and asymptotically optimal (in the maximin sense) parametric tests,...

This paper provides optimal testing procedures for the m-sample null hypothesis of Common Principal Components (CPC) under possibly non Gaussian and heterogenous elliptical densities. We first establish, under very mild assumptions that do not require finite moments of order four, the local...

This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudo-Gaussian robustifications by Tyler (1981,...

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary factorization property of this operator and propose a new Stein...

Abstract: We inscribe Stein's density approach for discrete distributionsin a new, exible framework, hereby extending and unifying a large portionof the relevant literature.We use this to derive a Stein identity whose powerwe illustrate by obtaining a wide variety of so-called inequalities...

We inscribe Stein's density approach for discrete distributions in a new, flexible framework, hereby extending and unifying a large portion of the relevant literature. We use this to derive a Stein identity whose power we illustrate by obtaining a wide variety of so-called inequalities between...

This article deals with Stein characterizations of probability distributions. We provide a general framework for interpreting these in terms of the parameters of the underlying distribution. In order to do so we introduce two concepts (a class of functions and an operator) which generalize those...