Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors

Aligned rank tests for the linear model with heteroscedastic errors

We consider the problem of testing subhypotheses in a heteroscedastic linear regression model. The proposed test statistics are based on the ranks of scaled residuals obtained under the null hypothesis. Any estimator that is n”2-consistent under the null hypothesis can be used to form the residuals. The error variances are estimated through a parametric model. This extends the theory of aligned...

Affine Invariant Multivariate Rank Tests for Several Samples

Affine invariant analogues of the two-sample Mann-Whitney-Wilcoxon rank sum test and the c-sample Kruskal-Wallis test for the multivariate location model are introduced. The definition of a multivariate (centered) rank function in the development is based on the Oja criterion function. This work extends bivariate rank methods discussed by Brown and Hettmansperger (1987a,b) and multivariate sign...

Full Rank Affine Invariant Submanifolds

Likelihood Ratio Tests in Multivariate Linear Model

The aim of this paper is to review likelihood ratio test procedures in multivariate linear models, focusing on projection matrices. It is noted that the projection matrices to the spaces spanned by mean vectors in hypothesis and alternatives play an important role. Some basic properties are given for projection matrices. The models treated include multivariate regression model, discriminant ana...

Rank-based Optimal Tests of the Adequacy of an Elliptic Varma Model

We are deriving optimal rank-based tests for the adequacy of a vector autoregressive-moving average (VARMA) model with elliptically contoured innovation density. These tests are based on the ranks of pseudo-Mahalanobis distances and on normed residuals computed from Tyler’s [Ann. Statist. 15 (1987) 234–251] scatter matrix; they generalize the univariate signed rank procedures proposed by Hallin...