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A functional central limit theorem on non-stationary random fields with nested spatial structure

Author

Listed:
  • Leshun Xu

    (University of Auckland
    Simon Fraser University)

  • Alan Lee

    (University of Auckland)

  • Thomas Lumley

    (University of Auckland)

Abstract

In this paper, we establish a functional central limit theorem on high dimensional random fields in the context of model-based survey analysis. For strongly-mixing non-stationary random fields, we provide an upper bound for the fourth moment of the finite population total. This inequality is the generalization of a key tool for proving functional central limit theorems in Rio (Asymptotic theory of weakly dependent random processes, Springer, Berlin, 2017). Under the nested sampling strategy, we introduce assumptions on strongly-mixing coefficients and quantile functions to show that a functional stochastic process asymptotically approaches to a Gaussian process.

Suggested Citation

  • Leshun Xu & Alan Lee & Thomas Lumley, 2023. "A functional central limit theorem on non-stationary random fields with nested spatial structure," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 215-234, April.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:1:d:10.1007_s11203-022-09273-9
    DOI: 10.1007/s11203-022-09273-9
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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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