Resample-smoothing and statistical learning for point processes

Abstract: 

The analysis of point patterns may almost always begin with estimating the intensity function due to its control over distributional behaviours of the  underlying point process that is assumed to have generated the observed pattern. Going through the literature, one can easily see that many techniques, based on different points of view, have been proposed for intensity estimation. In this talk, by employing independent random thinning, we show how i) a resample-smoothing approach can significantly improve the performance of Voronoi intensity estimators, and ii) a statistical-learning-based approach enhances kernel-based intensity estimators. We discuss  technical details, and through simulation studies show how our proposals improve the state-of-art. Applications to some real data will also be presented.

References:

Cronie, O., Moradi, M., and Biscio, C. A. (2021). Statistical learning and cross-validation for point processes. arXiv preprint arXiv:2103.01356.

Moradi, M., Cronie, O., Rubak, E., Lachieze-Rey, R., Mateu, J., and Baddeley, A. (2019). Resample-smoothing of Voronoi intensity estimators. Statistics and computing, 29(5), 995-1010.

To receive the Zoom link, please contact the seminar organiser: Priyantha Wijayatunga