Inference for the parameters of the complete symmetry covariance structure model

Abstract

A set of multivariate observations is said to have a complete symmetry covariance structure if each observation has covariance matrix Σ = θ₁I[subscript p] + θ₀J[subscript p]J'[subscript p] where θ₀ and θ₁ are unknown parameters. This study investigates the distributional properties of various test statistics for testing hypotheses and/or constructing confidence intervals about the parameters. It is known that an exact confidence interval and test exists for θ₁, based on its uniformly minimum variance estimator, but only approximate, simultaneous, or asymptotic confidence intervals and tests exist for θ₀. This study will show that the existing test statistics/confidence interval procedures for θ₀ are unsatisfactory under many conditions; the exact deficiencies of each procedure are discussed. New test statistics for θ₀ and θ₁ are developed in this research based on an asymptotic expansion of Browne's (1974) G.L.S. estimators, which are asymptotically normal. Results of a simulation study are presented which indicate the new improved test statistic for θ₀ provides improved inference over the existing test statistics/confidence interval procedures under many conditions.