Tests for the Dimensionality of the Regression Matrices When the Underlying Distributions are Elliptically Symmetric

摘要

In this paper, the authors derive likelihood ratio tests for the dimensionality of the regression matrices for the cases when the joint distributions of the observations are real and complex elliptically symmetric. The authors also derive asymptotic distributions of the above test statistics for two situations. In the first situation, the joint distribution of the observations is elliptically symmetric whereas the second situation assumes that the observations are distributed independently as elliptically symmetric. Keywords: Asymptotic distributions, Elliptically symmetric distributions, and Multivariate regression model.