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A Central Limit Theorem for linear random fields

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  • Mallik, Atul
  • Woodroofe, Michael

Abstract

A Central Limit Theorem is proved for linear random fields when sums are taken over union of finitely many disjoint rectangles. The approach does not rely upon the use of Beveridge-Nelson decomposition and the conditions needed are similar in nature to those given by Ibragimov for linear processes. When specializing this result to the case when sums are being taken over rectangles, a complete analogue of the Ibragimov result is obtained for random fields with a lot of uniformity.

Suggested Citation

  • Mallik, Atul & Woodroofe, Michael, 2011. "A Central Limit Theorem for linear random fields," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1623-1626, November.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:11:p:1623-1626
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    References listed on IDEAS

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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.
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    Cited by:

    1. Timothy Fortune & Magda Peligrad & Hailin Sang, 2021. "A local limit theorem for linear random fields," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 696-710, September.
    2. Peligrad, Magda & Sang, Hailin & Zhang, Na, 2024. "On the local limit theorems for linear sequences of lower psi-mixing Markov chains," Statistics & Probability Letters, Elsevier, vol. 210(C).
    3. Peligrad, Magda & Sang, Hailin & Xiao, Yimin & Yang, Guangyu, 2022. "Limit theorems for linear random fields with innovations in the domain of attraction of a stable law," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 596-621.

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