Estimates of the covariance matrix of vectors of \(U\)-statistics and confidence regions for vectors of Kendall's tau. (Q2810185)

The application of the asymptotic normality of \(U\)-statistics for the construction of asymptotic confidence regions requires the consistent estimation of the limiting covariance matrix. In the present paper such an estimator is proposed. Based on this proposal the author considers the construction of rectangular asymptotic confidence regions for vectors of Kendall's tau. These regions are products of intervals defined by a critical value from a multivariate normal distribution. The author proposes to compute this critical value by simulations. The advantage of rectangular regions is that they can be used for multiple comparisons.NEWLINENEWLINE The results are also applied to the construction of asymptotic confidence intervals for linear combinations of Kendall's population coefficients such as for the coefficient of agreement.NEWLINENEWLINE The proposed methods are demonstrated by a data example; coverage probabilities and length of intervals are estimated by simulations.