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A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields

Author

Listed:
  • Richard C. Bradley

    (Indiana University)

  • Cristina Tone

    (University of Louisville)

Abstract

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly $$\alpha $$ α -mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations.

Suggested Citation

  • Richard C. Bradley & Cristina Tone, 2017. "A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields," Journal of Theoretical Probability, Springer, vol. 30(2), pages 655-674, June.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:2:d:10.1007_s10959-015-0656-2
    DOI: 10.1007/s10959-015-0656-2
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    References listed on IDEAS

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    1. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
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    Cited by:

    1. Ruonan Xu & Jeffrey M. Wooldridge, 2022. "A Design-Based Approach to Spatial Correlation," Papers 2211.14354, arXiv.org.
    2. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    3. Thành, Lê Vǎn, 2024. "On Rio’s proof of limit theorems for dependent random fields," Stochastic Processes and their Applications, Elsevier, vol. 171(C).

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