Addressing non-normality in multivariate analysis using the t-distribution

Osorio, Felipe; Galea, Manuel; Henríquez, Claudio; Arellano–Valle, Reinaldo B.

doi:10.1007/s10182-022-00468-2

Cited by 2 publications

(3 citation statements)

References 31 publications

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“…Kotz and Nadarajah (2004)). In some papers the density function of the t p,ν -distribution is defined in a different form, where is the covariance matrix (Sutradhar (1993), Osorio et al (2023), for example). Note, however, that when testing covariance structures the behavior of the test statistics depends on the scale matrix , and the univariate multiplier in the expression for the covariance matrix in our definition does not influence the convergence properties of the statistics.…”

Section: Discussionmentioning

confidence: 99%

“…The discrepancy between normal and t p,ν distributions can be measured by, for example, negentropy (cf. Osorio et al (2023)), which for fixed degrees of freedom can be calculated as…”

Section: Convergence Of Test Statistics To the Limiting Distributionmentioning

confidence: 99%

“…12), for instance. Among many recent reports we refer to Osorio et al (2023) for applications in meteorology, Finegold and Drton (2011) for gene analysis, and Kan and Zhou (2017) and Galea et al (2020) for economic and financial applications. For risk estimation in portfolio theory, a multivariate t-distribution is specially advocated in Lauprete et al (2002) with reference to the t-copula.…”

Section: Introductionmentioning

confidence: 99%

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Covariance structure tests for multivariate t-distribution

Filipiak,

Kollo

2024

Stat Papers

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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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Section: Discussionmentioning

confidence: 99%

“…The discrepancy between normal and t p,ν distributions can be measured by, for example, negentropy (cf. Osorio et al (2023)), which for fixed degrees of freedom can be calculated as…”

Section: Convergence Of Test Statistics To the Limiting Distributionmentioning

confidence: 99%