PARAMETRIC AND NONPARAMETRIC ANALYSIS OF THE MULTIPLE DESIGN MULTIVARIATE LINEAR MODEL (SEEMINGLY UNRELATED REGRESSION EQUATIONS).

摘要

A generalized MANOVA model allowing for a different design matrix for each response variate is known as the multiple design multivariate (MDM) linear model. The MDM model may be applied, for example, to a system of regression equations consisting of polynomial models of varying degree.; Parametric aspects of the MDM model have been investigated extensively in both the biometric and econometric literature. In contrast, nonparametric procedures for the MDM model have not yet been developed.; In the present research, a Monte Carlo simulation experiment is conducted to further examine the small sample properties of three alternative estimators under the MDM model. The estimators examined are (single-equation) ordinary least squares, Zellner's two-stage Aitken estimator and Zellner's iterative Aitken estimator. The simulation study focuses on the relative efficiencies of the alternative estimators under various experimental conditions.; The present research also considers the application of nonparametric theory to the MDM linear model. Based on the work of Chatterjee and Sen (1964), Hajek (1961, 1968) and Puri and Sen (1969), a linear rank statistic is constructed and its unconditional asymptotic multi-normality under a suitable null hypothesis is established. Large-sample tests for general linear hypotheses are then developed. Finally, an application to a repeated measures design with changing covariate values is considered.