Inference Based on Ranks for the Multiple-Design Multivariate Linear Model

Abstract

Abstract Multivariate models more general than the standard multivariate linear model have received considerable attention in both the statistical and econometric literature; see Srivastava (1966, 1967, 1968) and Kleinbaum (1973). The multiple-design multivariate (MDM) linear model generalizes the standard multivariate linear model in the sense that a different design matrix is used for each response (dependent) variable. Important applications of the MDM linear model include changing covariates in repeated measurement designs and p-variate regression systems (p > 1) with different regressors for each of the p response variables. The latter situation has been described as “seemingly unrelated regression equations” in the econometric literature (Zellner 1962). In this article an approach to statistical inference is presented under the MDM linear model based on multivariate rank and aligned rank statistics. In Section 1 estimation and hypothesis testing for the MDM linear model are reviewed under parametric...