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Parametric estimation of spatial–temporal point processes using the Stoyan–Grabarnik statistic

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Abstract

A novel estimator for the parameters governing spatial–temporal point processes is proposed. Unlike the maximum likelihood estimator, the proposed estimator is fast and easy to compute, and does not require the computation or approximation of a computationally expensive integral. This parametric estimator is based on the Stoyan–Grabarnik (sum of inverse intensity) statistic and is shown to be consistent, under quite general conditions. Simulations are presented demonstrating the performance of the estimator.

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Acknowledgements

Thanks to Adrian Baddeley for suggesting estimation based on kernel smoothing the scaled residual field, to Peter Diggle for suggesting the partial likelihood as an alternative way of avoiding having to compute the integral in the MLE, to Aila Saarka for suggesting that the SG estimator could be used to obtain starting values for the MLE, and to James Molyneux for his work on selecting partitions. This material is based upon work supported by the National Science Foundation under grant number DMS-2124433.

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  1. UCLA Department of Statistics, 8125 Math-Science Building, Los Angeles, CA, 90095, USA

    Conor Kresin & Frederic Schoenberg

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  1. Conor Kresin
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  2. Frederic Schoenberg
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Correspondence to Frederic Schoenberg.

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Kresin, C., Schoenberg, F. Parametric estimation of spatial–temporal point processes using the Stoyan–Grabarnik statistic. Ann Inst Stat Math 75, 887–909 (2023). https://doi.org/10.1007/s10463-023-00866-6

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  • DOI: https://doi.org/10.1007/s10463-023-00866-6

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