Consistency of the Hotelling-, wilks- Roy- and pillai-tests for a general linear hypothesis in multiyariate linear nonnormally Distribnted models

Abstract

In multivariate linear not necessary normally distributed models with expectation X_nB and covariance ∑ ⊗ I_n for any n ∈ 𝔫 the testing prob!em H: "ABF =G" against K: "ABF ¦G" is considered. Sufficient conditions are derived for consistency of the asymptotic HOTELLING-, WILKS-, ROY- and PILLAI-test. In the normal case these conditions of consistency of the asymptotic as well as of the usual exact tests can be weakened.