Kybernetika 52 no. 2, 280-293, 2016

Estimates of covariance matrix of U-statistic and confidence intervals for Kendall tau

František RublíkDOI: 10.14736/kyb-2016-2-0280


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.


U-statistics, vector of Kendall's coefficients, coefficient of agreement, confidence interval, consistent estimate of asymptotic covariance matrix


62G05, 62G15


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