Sensitivity Analysis for the Decomposition of Mixed Partitioned Multivariate Models into Two Seemingly Unrelated Submodels

Abstract

The paper is focused on the decomposition of mixed partitioned multivariate models into two seemingly unrelated submodels in order to obtain more efficient estimators. The multiresponses are independently normally distributed with the same covariance matrix. The partitioned multivariate model is considered either with, or without an intercept. The elimination transformation of the intercept that preserves the BLUEs of parameter matri- ces and the MINQUE of the variance components in multivariate models with and without an intercept is stated. Procedures on testing the decomposition of the partitioned model are presented. The properties of plug-in test statistics as functions of variance compo- nents are investigated by sensitivity analysis and insensitivity regions for the significance level are proposed. The insensitivity region is a safe region in the parameter space of the variance components where the approximation of the variance components can be used without any essential deterioration of the significance level of the plug-in test statistic. The behavior of plug-in test statistics and insensitivity regions is studied by simulations.