Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 735436, 18 pages
doi:10.1155/2008/735436
Abstract
Let F^n
be an estimator obtained by integrating a kernel type density estimator based
on a random sample of size n. A central limit theorem is established for the target
statistic F^n(ξ^n), where the underlying random vector forms an asymptotically stationary
absolutely regular stochastic process, and
ξ^n
is an estimator of a multivariate parameter
ξ
by using a vector of U-statistics. The results obtained extend or generalize previous
results from the stationary univariate case to the asymptotically
stationary multivariate case. An example of asymptotically
stationary absolutely regular multivariate ARMA process and an example of a useful
estimation of F(ξ) are given in the applications.