kppmenet: combining the kppm and elastic net regularization for inhomogeneous Cox point process with correlated covariates

Abstract

The $\mathrm{kppm}$ is a standard procedure to estimate the parameters of the inhomogeneous Cox point process. However, the procedure cannot handle the problem when the models involve correlated covariates. In this study, we develop the $\mathrm{kppmenet}$, the modified version of the $\mathrm{kppm}$, for the inhomogeneous Cox point process involving correlated covariates by considering elastic net regularization. We compare the methodology in a simulation study and apply it to model major-shallow earthquake distribution in Sumatra, Indonesia. We conclude that the $\mathrm{kppmenet}$ outperforms $\mathrm{kppm}$ when correlated covariates are involved.

Keywords: Earthquake modelling; lasso; natural disaster; spatial point process; $\mathtt{spatstat}$$\mathtt{R}$ package.