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

Leshun Xu, Alan Lee () and Thomas Lumley ()
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Leshun Xu: University of Auckland
Alan Lee: University of Auckland
Thomas Lumley: University of Auckland

Statistical Inference for Stochastic Processes, 2023, vol. 26, issue 1, No 8, 215-234

Abstract: 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.

Keywords: Functional central limit theorem; Strongly-mixing coefficient; Nested sampling method; Random fields (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11203-022-09273-9

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