Estimates of the covariance matrix of vectors of u-statistics and confidence regions for vectors of Kendall's tau

Rublík, František. "Estimates of the covariance matrix of vectors of u-statistics and confidence regions for vectors of Kendall's tau." Kybernetika 52.2 (2016): 280-293. <http://eudml.org/doc/281534>.

@article{Rublík2016,
abstract = {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.},
author = {Rublík, František},
journal = {Kybernetika},
keywords = {consistent estimate of asymptotic covariance matrix; U-statistics; vector of Kendall's coefficients; coefficient of agreement; confidence interval; consistent estimate of asymptotic covariance matrix; -statistics; vector of Kendall's coefficients; coefficient of agreement; confidence interval},
language = {eng},
number = {2},
pages = {280-293},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Estimates of the covariance matrix of vectors of u-statistics and confidence regions for vectors of Kendall's tau},
url = {http://eudml.org/doc/281534},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Rublík, František
TI - Estimates of the covariance matrix of vectors of u-statistics and confidence regions for vectors of Kendall's tau
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 2
SP - 280
EP - 293
AB - 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.
LA - eng
KW - consistent estimate of asymptotic covariance matrix; U-statistics; vector of Kendall's coefficients; coefficient of agreement; confidence interval; consistent estimate of asymptotic covariance matrix; -statistics; vector of Kendall's coefficients; coefficient of agreement; confidence interval
UR - http://eudml.org/doc/281534
ER -