Score Tests for Intercept and Slope Parameters of Doubly Multivariate Linear Models with Skew-Normal Errors

Abstract

We generalize the theory of linear models for doubly multivariate data from matrixvariate normally distributed errors to matrix-variate skew normally distributed errors. In addition, we assume that the covariance matrix defining the locationscale matrix-variate skew normal distribution has block compound symmetry structure. We derive the maximum likelihood estimators of the model's parameters; the Fisher information matrix for the direct, working, and centered parametrizations; Rao's score tests and likelihood ratio tests for model building tests of hypotheses; and a hypothesis test for the centered intercept. A profiling argument is used to reduce the dimensionality of the optimization method used to obtain the maximum likelihood estimators and a comprehensive discussion of initial values is provided. Finally, we provide a real-world example to illuminate these derivations and apply a goodness-of-fit test to validate the distributional assumption.

More on the Supremum Statistic to Test Multivariate Skew-Normality

“…We will extend the supremum test statistic to test the skew-normality of doubly multivariate data with Kronecker product covariance structure and report it in a future correspondence. Recently, Opheim and Roy [18] developed doubly multivariate linear models with matrix-variate skew-normally distributed errors by assuming that the covariance matrix defining the location-scale matrix-variate skew-normal distribution has block compound symmetry structure.…”