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.
The paper is concerned with estimation of the probability function of a discrete random variable by minimizing the Shannon quasi-norm while meeting the moment conditions for the probability function estimated. After describing this method in detail, the paper further focuses on deriving confidence intervals for probabilities and possible application of these methods to particular data sets. and Obsahuje seznam literatury