A method to estimate the center intensity of an inhomogeneous Poisson cluster process

A method to estimate the intensity function of a time inhomogeneous Poisson cluster process from observed times is developed from methods used to estimate intensity functions in ordinary inhomogeneous Poisson processes. The estimate is based on a kernel method used in density estimation scaled by the probability that an observation belongs to the cluster center process. This probability is estimated using a sequential imputation method developed by Kong, Liu and Wong. An automatic procedure to select the bandwidths for the kernel is also derived, using likelihood cross-validation and the EM algorithm. A bootstrap procedure to obtain standard errors for the estimates is also derived.;The method is applied to a small selection of input signals for an application in the estimation of radon concentration. Although computationally intensive, the method obtains less variable estimates for that particular application than the method already in use. Effects of adding a naive boundary correction to the estimates, and of using different functional forms for the kernels are also examined.;A method already in use to obtain estimates of radon concentration for aggregate data is shown to be equivalent to the method of moments under certain assumptions.