Testing Hypotheses for Variance Components in Mixed Linear Models

Michalski, Andrzej; Zmyślony, Roman

doi:10.1080/02331889708802533

Cited by 43 publications

(25 citation statements)

References 8 publications

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“…In the univariate case, for mixed models with an algebraic structure based on a commutative quadratic subspace, testing hypotheses about a single real parameter is based on unbiased estimators. Following the ideas in [20] and in [5], for a single variance-covariance matrix 0 (just multivariate case), we take the sum of the positive components of the estimator of 0 and the sum of the negative components of the estimator of 0 and then their ratio as a test statistic. One can adapt this idea to the doubly multivariate case, assuming that 1 = 0 under the null hypothesis, while all parameters of 1 are positive under the alternative hypothesis.…”

Section: Discussionmentioning

confidence: 99%

Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure

Roy

Zmyślony

Fonseca

et al. 2016

Journal of Multivariate Analysis

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a b s t r a c tThe paper deals with the best unbiased estimators of the blocked compound symmetric covariance structure for m-variate observations over u sites under the assumption of multivariate normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matrices. Complete statistics are then derived to prove that the estimators are best unbiased. Finally, strong consistency is proven. The proposed method is implemented with a real data set.

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Section: Discussionmentioning

confidence: 99%

Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure

Roy

Zmyślony

Fonseca

et al. 2016

Journal of Multivariate Analysis

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“…This has led to the introduction of generalized F-tests. The statistics for these tests are given by the quotients of linear combinations of independent chi-squares both in the numerator and denominator and were introduced by Michalski and Zmyślony [2,3]. Results on these distributions were obtained first for the central case, in [4], and then for the non-central case, in [5].…”

Section: Introductionmentioning

confidence: 99%

Control of the truncation errors for generalizedFdistributions

Nunes

Ferreira

Mexia

2012

Journal of Statistical Computation and Simulation

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F-tests may not be used for all relevant hypothesis, even in rather simple models, which led to the introduction of generalized F-tests. The statistics of these tests are quotients of linear combinations of independent chi-squares, which may be non-central. When the observations are collected under non-standardized conditions, the non-centrality parameters may be random. The generalized F distributions are given by infinite sums. In this study, we show that there is an excellent control of the truncations errors for those sums. The case in which the non-centrality parameters have Gamma distributions is singled out.

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“…When that number is superior to one, even assuming normality, we cannot use the usual F tests for testing the nullity of variance components. We then must apply generalized F tests, that were introduced by Michalski and Zmyśloni (1996) and Michalski and Zmyśloni (1999), first for variance components and then for the fixed effects part of mixed models. The main idea beyond these tests is that given a quadratic unbiased estimator of a parameter θ , we take the quotient of the positive by the negative part of the estimator as a statistic for testing…”

Section: Introductionmentioning

confidence: 99%