Multivariate Generalized Linear-statistics of short range dependent data

摘要

Generalized linear (GL-) statistics are defined as functionals of anU-quantile process and unify different classes of statistics such asU-statistics and L-statistics. We derive a central limit theorem forGL-statistics of strongly mixing sequences and arbitrary dimension of theunderlying kernel. For this purpose we establish a limit theorem forU-statistics and an invariance principle for U-processes together with aconvergence rate for the remaining term of the Bahadur representation. Anapplication is given by the generalized median estimator for the tail-parameterof the Pareto distribution, which is commonly used to model exceedances of highthresholds. We use subsampling to calculate confidence intervals andinvestigate its behaviour under independence and strong mixing in simulations.