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标题：Central Limit Theorems For Weighted Sums Of A Spatial Process Under A Class Of Stochastic And Fixed Designs
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作者：S.N. LAHIRI ; Iowa State University, Ames, USA
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2003
卷号：65
期号：02
出版社：Indian Statistical Institute
摘要：Let $\{Z(\bfs):\bfs\in\Re^d\}$ be a zero mean stationary random field which is observed at a finite number of locations. % $\bf s_1,\ldots,\bf s_{n}$. In this paper, Central Limit Theorems are proved for weighted sums of the form %$\sum_{i=1}^{n} $\sum_i \omega_n(\bfs_i)Z(\bfs_i)$ where the locations $\bfs_i$'s are specified by certain stochastic spatial designs driven by sequences of iid random vectors. A complete description of the effects of the underlying spatial sampling design on the asymptotic variance of the sum is given. Furthermore, results are also proved for a class of nonrandom spatial designs based on grids under the {\it mixed increasing-domain} spatial asymptotic structure that involves simultaneous {\it infilling} of increasing domains.
关键词：Central limit theorem, infill sampling, increasing-domain asymptotics, long range dependence, random field, strong mixing, stochastic design, spatial design.