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Estimates of the covariance matrix of vectors of u-statistics and confidence regions for vectors of Kendall's tau
Kybernetika, Tome 52 (2016) no. 2, pp. 280-293 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Consistent estimators of the asymptotic covariance matrix of vectors of $U$-statistics are used in constructing asymptotic confidence regions for vectors of Kendall's correlation coefficients corresponding to various pairs of components of a random vector. The regions are products of intervals computed by means of a critical value from multivariate normal distribution. The regularity of the asymptotic covariance matrix of the vector of Kendall's sample coefficients is proved in the case of sampling from continuous multivariate distribution under mild conditions. The results are applied also to confidence intervals for the coefficient of agreement. The coverage and length of the obtained (multivariate) product of intervals are illustrated by simulation.
Consistent estimators of the asymptotic covariance matrix of vectors of $U$-statistics are used in constructing asymptotic confidence regions for vectors of Kendall's correlation coefficients corresponding to various pairs of components of a random vector. The regions are products of intervals computed by means of a critical value from multivariate normal distribution. The regularity of the asymptotic covariance matrix of the vector of Kendall's sample coefficients is proved in the case of sampling from continuous multivariate distribution under mild conditions. The results are applied also to confidence intervals for the coefficient of agreement. The coverage and length of the obtained (multivariate) product of intervals are illustrated by simulation.
DOI : 10.14736/kyb-2016-2-0280
Classification : 62G05, 62G15
Keywords: consistent estimate of asymptotic covariance matrix; U-statistics; vector of Kendall's coefficients; coefficient of agreement; confidence interval 
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Rublík, František. Estimates of the covariance matrix of vectors of u-statistics and confidence regions for vectors of Kendall's tau. Kybernetika, Tome 52 (2016) no. 2, pp. 280-293. doi: 10.14736/kyb-2016-2-0280

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