Covariance Structure Tests for t-distribution

Kollo, Tõnu; Valge, Marju

doi:10.1007/978-3-030-56773-6_12

Recent Developments in Multivariate and Random Matrix Analysis 2020

DOI: 10.1007/978-3-030-56773-6_12

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Covariance Structure Tests for t-distribution

Tõnu Kollo

Marju Valge

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2024

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Covariance structure tests for multivariate t-distribution

Filipiak,

Kollo

2024

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We derive an equation system for finding Maximum Likelihood Estimators (MLEs) for the parameters of a p-dimensional t-distribution with $$\nu $$ ν degrees of freedom, $$t_{p,\nu }$$ t p , ν , and use the MLEs for testing covariance structures for the $$t_{p,\nu }$$ 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 $$\textrm{H}_0:\varvec{\Sigma }=\varvec{\Sigma }_0$$ H 0 : Σ = Σ 0 , using a matrix derivative technique. Here the $$p\times p$$ p × p -matrix $$\varvec{\Sigma }$$ 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 $$t_{p,\nu }$$ 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.

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Covariance structure tests for multivariate t-distribution

Filipiak,

Kollo

2024

Stat Papers

Self Cite

View full text Add to dashboard Cite

show abstract

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Covariance Structure Tests for t-distribution

Cited by 1 publication

References 7 publications

Covariance structure tests for multivariate t-distribution

Covariance structure tests for multivariate t-distribution

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