Rates in the CLT for sums of dependent multiindexed random vectors (Q1781661)

The authors prove a number of CLT type results for the partial sums of dependent random vectors from a multiindexed random field. The underlying dependency structure is specified according to a concept of \textit{P. Doukhan} and \textit{S. Louhichi} [Stochastic Processes Appl. 84, No.~2, 313--342 (1999; Zbl 0996.60020)] for stochastic processes and of \textit{A. Bulinski} and \textit{C. Suquet} [Stat. Probab. Lett. 54, No.~2, 215--226 (2001; Zbl 0989.60052)] for random fields. Explicit bounds for the weak convergence rates are established. An application to the kernel estimate for the density of a multivariate stationary random field is also provided.