Sufficient dimension reduction for spatial point processes using weighted principal support vector machines

We consider sufficient dimension reduction (SDR) for spatial point processes. SDR methods aim to identify a lower dimensional sufficient subspace of a data set, in a modelfree manner. Most SDR results are based on independent data, and also often do not work well with binary data. [13] introduced a SDR framework for spatial point processes by characterizing point processes as a binary process, and applied several popular SDR methods to spatial point data. On the other hand, [29] proposed Weighted Principal Support Vector Machines (WPSVM) for SDR and showed that it performed better than other methods with binary data. We combine these two works and examine WPSVM for spatial point processes. We show consistency and asymptotic normality of the WPSVM estimated sufficient subspace under some conditions on the spatial process, and compare it with other SDR methods via a simulation study and an application to real data.