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

Conor Kresin () and Frederic Schoenberg ()
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Conor Kresin: UCLA Department of Statistics
Frederic Schoenberg: UCLA Department of Statistics

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 6, No 1, 887-909

Abstract: 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.

Keywords: Conditional intensity; Cox process; Hawkes process; Maximum likelihood estimation; Poisson process; Space-time point process (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-023-00866-6

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