The authors consider multivariate analysis of variance procedures based on the multivariate spatial ranks. Two models are considered: the location-family model and the fully nonparametric model. Procedures for testing main and interaction effects are given for the 2 × 2 layout.

A popular nonparametric measure of a monotone relation between two variables is Kendall's tau. Originally, most analysis of this statistic assumed the two variables were independent, while more recently there has been interest in finding "nonnull" models for the observations which allow types of...

Data do not always obey the normality assumption, and outliers can have dramatic impacts on the quality of the least squares methods. We use Huber's loss function in developing robust methods for time-course multivariate responses. We use spline basis expansion of the time-varying regression...

The problem of testing equality of two normal covariance matrices, [Sigma]1 = [Sigma]2 is studied. Two alternative hypotheses, [Sigma]1 [not equal to] [Sigma]2 and [Sigma]1 - [Sigma]2 0 are considered. Minimal complete classes among the class of invariant tests are found. The group of...

Robust estimates of principal components are developed using appropriate definitions of multivariate signs and ranks. Simulations and a data example are used to compare these methods to the regular method and one based on the minimum-volume-ellipsoid estimate of the covariance matrix. The sign...