Weighted likelihood estimators for point processes

Based on the technique of residual analysis, a weighted likelihood estimator for temporal and spatiotemporal point processes is proposed. Similarly, weighted Poisson likelihood estimators and weighted pseudo-likelihood estimators for spatial point processes are also proposed. The weighted likelihood estimator is applied to the spatiotemporal Epidemic Type Aftershock Sequence (ETAS) model to study the spatial variations of seismicity characteristics in the Japan region.