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A central limit theorem for stationary random fields

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  • El Machkouri, Mohamed
  • Volný, Dalibor
  • Wu, Wei Biao
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    Abstract

    This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form Xk=g(εk−s,s∈Zd), k∈Zd, where (εi)i∈Zd are iid random variables and g is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying domain on which the process is observed. A limit theorem for the sample auto-covariance function is also established.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 1 ()
    Pages: 1-14

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:1-14

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    Related research

    Keywords: Central limit theorem; Spatial processes; m-dependent random fields; Weak mixing;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Paulauskas, Vygantas, 2010. "On Beveridge-Nelson decomposition and limit theorems for linear random fields," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 621-639, March.
    2. El Machkouri, Mohamed, 2002. "Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 285-299, December.
    3. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
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    Cited by:
    1. Wang, Yizao & Woodroofe, Michael, 2014. "On the asymptotic normality of kernel density estimators for causal linear random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 201-213.

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