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Score, pseudo-score and residual diagnostics for spatial point process models. (English) Zbl 1332.62363
Summary: We develop new tools for formal inference and informal model validation in the analysis of spatial point pattern data. The score test is generalized to a “pseudo-score” test derived from Besag’s pseudo-likelihood, and to a class of diagnostics based on point process residuals. The results lend theoretical support to the established practice of using functional summary statistics, such as Ripley’s \(K\)-function, when testing for complete spatial randomness; and they provide new tools such as the compensator of the \(K\)-function for testing other fitted models. The results also support localization methods such as the scan statistic and smoothed residual plots. Software for computing the diagnostics is provided.

MSC:
62M30 Inference from spatial processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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