Multivariate Signed-Rank Tests in Vector Autoregressive Order Identification

Multivariate Signed-Rank Tests in Vector Autoregressive Order Identification

The classical theory of rank-based inference is essentially limited to univariate linear models with independent observations. The objective of this paper is to illustrate some recent extensions of this theory to time-series problems (serially dependent observations) in a multivariate setting (multivariate observations) under very mild distributional assumptions (mainly, elliptical symmetry; fo...

Multivariate Generalized Spatial Signed-Rank Methods

New multivariate generalized signed-rank tests for the one sample location model having favorable efficiency and robustness properties are introduced and studied. Limiting distributions of the tests and related estimates as well as formulae for asymptotic relative efficiencies are found. Relative efficiencies with respect to the classical Hotelling T 2 test (and the mean vector) are evaluated f...

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...

A bivariate first-order signed integer-valued autoregressive process

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, ...