Asymptotic Properties of Nonparametric Intensity Estimation for Replicated Spatial Point Patterns

A kernel-type nonparametric estimator of the intensity function for inhomogeneous spatial point patterns with replicated data is proposed. Asymptotic expansion of the mean square error is derived and the rate of convergence of the integrated square error is also investigated. Two methods, least-square and composite likelihood cross-validation, for selecting the bandwidth are described. The performance of the two procedures are illustrated using simulation data.