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Randomized multivariate Central Limit Theorems for ergodic homogeneous random fields

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  • Tempelman, Arkady

Abstract

We present new versions of the CLT which are valid for each ergodic homogeneous multivariate random field (X1(⋅),…,Xd(⋅)) on Rm or Zm(m≥1) (in particular, for each ergodic stationary random process and for each ergodic stationary random sequence) such that for all l E[|Xl(0)|2+δ]<∞ for some δ>0(l=1,...,d); in some statements ergodicity is not assumed. Randomization made it possible to significantly weaken the strong mixing conditions and other restrictions of dependence, that are imposed in the conventional CLTs. These results pave the way to consistent statistical inference for homogeneous random fields and stationary processes with strong dependence.

Suggested Citation

  • Tempelman, Arkady, 2022. "Randomized multivariate Central Limit Theorems for ergodic homogeneous random fields," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 89-105.
    • Handle: RePEc:eee:spapps:v:143:y:2022:i:c:p:89-105
    DOI: 10.1016/j.spa.2021.10.006
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    References listed on IDEAS

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    1. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 1-14.
    2. Peligrad, Magda & Zhang, Na, 2018. "On the normal approximation for random fields via martingale methods," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1333-1346.
    3. Volný, Dalibor & Wang, Yizao, 2014. "An invariance principle for stationary random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4012-4029.
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