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A caution on mixing conditions for random fields

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  • Bradley, Richard C.

Abstract

For strictly stationary random fields, some obvious versions of the ø-mixing and absolute regularity conditions turn out to be equivalent to versions of m-dependence.

Suggested Citation

  • Bradley, Richard C., 1989. "A caution on mixing conditions for random fields," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 489-491, October.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:5:p:489-491
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    Citations

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    Cited by:

    1. Richard C. Bradley, 2001. "A Stationary Rho-Mixing Markov Chain Which Is Not “Interlaced” Rho-Mixing," Journal of Theoretical Probability, Springer, vol. 14(3), pages 717-727, July.
    2. Nguyen, Hien D. & McLachlan, Geoffrey J., 2018. "Chunked-and-averaged estimators for vector parameters," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 336-342.
    3. Daniel Nordman, 2008. "An empirical likelihood method for spatial regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 351-363, November.
    4. S. N. Lahiri, 2018. "Uncertainty Quantification in Robust Inference for Irregularly Spaced Spatial Data Using Block Bootstrap," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 173-221, December.
    5. S. Lahiri & Kanchan Mukherjee, 2004. "Asymptotic distributions of M-estimators in a spatial regression model under some fixed and stochastic spatial sampling designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 225-250, June.
    6. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    7. Burton, Robert M. & Steif, Jeffrey E., 1995. "Quite weak Bernoulli with exponential rate and percolation for random fields," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 35-55, July.
    8. Bradley, Richard C., 1997. "Every "lower psi-mixing" Markov chain is "interlaced rho-mixing"," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 221-239, December.
    9. Salim Bouzebda, 2024. "Limit Theorems in the Nonparametric Conditional Single-Index U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 12(13), pages 1-81, June.
    10. 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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