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Statistical inference on stationary shot noise random fields

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  • Antoine Lerbet

    (Université de Tours)

Abstract

We study the asymptotic behaviour of a stationnary shot noise random field. We use the notion of association to prove the asymptotic normality of the moments and a multidimensional version for the correlation functions. The variance of the moment estimates is detailed as well as their correlation. When the field is isotropic, the estimators are improved by reducing the variance. These results will be applied to the estimation of the model parameters in the case of a Gaussian kernel, with a focus on the correlation parameter. The asymptotic normality is proved and a simulation study is carried out.

Suggested Citation

  • Antoine Lerbet, 2023. "Statistical inference on stationary shot noise random fields," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 551-580, October.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:3:d:10.1007_s11203-023-09294-y
    DOI: 10.1007/s11203-023-09294-y
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    References listed on IDEAS

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    1. Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
    2. Elena Di Bernardino & Céline Duval, 2022. "Statistics for Gaussian random fields with unknown location and scale using Lipschitz‐Killing curvatures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 143-184, March.
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