Displaying similar documents to “Estimates of the covariance matrix of vectors of u-statistics and confidence regions for vectors of Kendall's tau”

Hypothesis testing in unbalanced two-fold nested random models

Marcin Przystalski (2016)

Applicationes Mathematicae

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In many applications of linear random models to multilevel data, it is of interest to test whether the random effects variance components are zero. In this paper we propose approximate tests for testing significance of variance components in the unbalanced two-fold nested random model in the presence of non-normality. In the derivations of the asymptotic distributions of the test statistics, as an intermediate result, the explicit form of the asymptotic covariance matrix of the vector...

Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

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By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant | σ 2 ∑ | in the MGM model ( U , X B , σ 2 ∑ ⊗ V ) , ∑ > 0 , scalar σ 2 > 0 , with a matrix V ≥ 0 . A known n × p random matrix U has the expected value E ( U ) = X B , where the n × d matrix X is a known matrix of an experimental design, B is an unknown d × p matrix of parameters and σ 2 ∑ ⊗ V is the covariance matrix of U , ⊗ being the symbol...

Asymptotic properties of the growth curve model with covariance components

Ivan Žežula (1997)

Applications of Mathematics

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We consider a multivariate regression (growth curve) model of the form Y = X B Z + ε , E ε = 0 , var ( vec ε ) = W ⊗ Σ , where W = ∑ i = 1 k θ i V i and θ i ’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters { B i j } estimating simultaneously the first and the second order parameters.

Stress-strength based on m -generalized order statistics and concomitant for dependent families

Filippo Domma, Abbas Eftekharian, Mostafa Razmkhah (2019)

Applications of Mathematics

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The stress-strength model is proposed based on the m -generalized order statistics and the corresponding concomitant. For the dependency between m -generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional...

Some limit behavior for linear combinations of order statistics

Yu Miao, Mengyao Ma (2021)

Kybernetika

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In the present paper, we establish the moderate and large deviations for the linear combinations of uniform order statistics. As applications, the moderate and large deviations for the k -th order statistics from uniform distribution, Gini mean difference statistics and the k -th order statistics from general continuous distribution are obtained.

Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

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The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. 1 ∘ determinant ratios as products of independent chi-square distributions, 2 ∘ moments for the determinants and 3 ∘ the method of obtaining approximate densities of the determinants.