Density estimation for point processes

A general nonparametric density estimation problem is considered in which the data is generated by a spatial point process. Several practical problems are special cases of it, including those of estimating the common probability density of a sequence of random vectors and estimating the product density of a stationary multivariate point process. Kernel and k-nearest neighbor estimators are defined and in each case the joint asymptotic normality and consistency of the estimates of the density at a given finite number of points is derived.