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Practically Applicable Central Limit Theorem for Spatial Statistics

Authors
Park, Byeong U.Kim, Tae YoonPark, Jeong-SooHwang, S. Y.
Issue Date
Jul-2009
Publisher
SPRINGER HEIDELBERG
Keywords
Central limit theorem; Nearly infill domain sampling; Density estimation
Citation
MATHEMATICAL GEOSCIENCES, v.41, no.5, pp 555 - 569
Pages
15
Journal Title
MATHEMATICAL GEOSCIENCES
Volume
41
Number
5
Start Page
555
End Page
569
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/13726
DOI
10.1007/s11004-008-9184-2
ISSN
1874-8961
1874-8953
Abstract
Let {Z(s):saDaS dagger a"e (d) } be a zero mean stationary random field observed at a finite number of locations. Lahiri (Sankhya Ser. A 65:356-388, 2003) proved spatial central limit theorems (CLT) for a (i=1) (n) Z(s (i) ) assuming a 'nearly infill domain sampling'. Applications of his results depended on the underlying spatial sampling region and the design in a complicated fashion. The main objective of this paper is to provide CLTs that could be applied easily in practice. We present two main results assuming a 'nearly infill domain sampling' defined mainly in terms of dependence. Theorem 1 establishes a CLT for a (i=1) (n) Z(s (i) ) and Theorem 2 is obtained mainly for applications to density estimates. We report on a simulation study for illustrating a way of applying our results in practice.
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