Central Limit Theorem of the Smoothed Empirical Distribution Functions for Asymptotically Stationary Absolutely Regular Stochastic Processes

[摘要] LetF∧nbe an estimator obtained by integrating a kernel type density estimator basedon a random sample of sizen. A central limit theorem is established for the targetstatisticF∧n(ξ∧n), where the underlying random vector forms an asymptotically stationaryabsolutely regular stochastic process, andξ∧nis an estimator of a multivariate parameterξby using a vector of U-statistics. The results obtained extend or generalize previousresults from the stationary univariate case to the asymptoticallystationary multivariate case. An example of asymptoticallystationary absolutely regular multivariate ARMA process and an example of a usefulestimation ofF(ξ)are given in the applications.

[学科分类] 应用数学