Covariance structure tests formultivariate t-distribution
[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee
2024
scientific article
english
- multivariate t-distribution
- covariance structure testing
- likelihood ratio test
- Rao score test
- Wald test
- wielowymiarowy rozkład t
- testowanie struktury kowariancji
- test ilorazu wiarogodności
- test Rao
- test Walda
EN We derive an equation system for finding Maximum Likelihood Estimators (MLEs) for the parameters of a p-dimensional t-distribution with ν degrees of freedom, t p,ν , and use the MLEs for testing covariance structures for the t p,ν -distributed population. The likelihood ratio test (LRT), Rao score test (RST) and Wald test (WT) statistics are derived under the general null-hypothesis H0 : Σ = Σ0 , using a matrix derivative technique. Here the p× p-matrix Σ is a dispersion/scale parameter. Convergence to the asymptotic chi-square distribution under the null hypothesis is examined in extensive simulation experiments. Also the convergence to the chi-square distribution is studied empirically in the situation when the MLEs of a t p,ν -distribution are changed to the corresponding estimators for a normal population. Type I errors and the power of the tests are also examined by simulation. In the simulation study the RST behaved more adequately than all remaining statistics in the situation when the dimensionality p was growing.
4537 - 4566
CC BY (attribution alone)
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