Rank-Based Methods for Multivariate Linear Models

Abstract

Rank-based methods are used to develop a theory for the multivariate linear model analogous to least squares. Quadratic procedures for testing H[β₀β′]′K = 0 are considered both with and without the assumption of Symmetrie errors. When testing the hypothesis HβK = 0, the reduced-model R estimate is shown to be asymptotically a linear function of the full-model R estimate. Three asymptotically equivalent test procedures are developed: quadratic, aligned rank, and drop in dispersion. An analysis of covariance example is considered using both rank and least squares procedures.

KEY WORDS:

• Aligned rank statistics
• Linear models
• Multivariate analysis
• R estimates
• Rank tests