On Testing Structures of the Covariance Matrix: A Non-normal Approach

Kollo, Tõnu; Valge, Marju

doi:10.1007/978-3-030-83670-2_12

Cited by 1 publication

(3 citation statements)

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“…It is also worth noting that similar conclusions were reached by Kollo et al (2016), where multivariate normality of the distribution of the observation matrix was assumed, i.e., the convergence of RST to the limiting chi-square distribution is quicker than with LRT and WT.…”

Section: Convergence Of Test Statistics To the Limiting Distributionsupporting

confidence: 59%

“…Thus, the formula for RST reduces to the formula for RST under normality RST → n 2 tr (I p − S −1 0 ) 2 ; cf. Kollo et al (2016).…”

Section: Propositionmentioning

confidence: 99%

“…In practice the uncorrected test is still used. In Kollo et al (2016) it is shown that instead of the LRT or Wald test (WT), the more consistent Rao score test (RST) should be used to test a particular covariance structure under normality. In this paper we examine these three tests for a multivariate t p,ν -distributed population.…”

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: Convergence Of Test Statistics To the Limiting Distributionsupporting

confidence: 59%

“…Thus, the formula for RST reduces to the formula for RST under normality RST → n 2 tr (I p − S −1 0 ) 2 ; cf. Kollo et al (2016).…”

Section: Propositionmentioning

confidence: 99%