Orthogonal Polynomial Estimates for Point Process Densities

摘要

An algorithm is described for estimating first order densities by an approximate finite series expansion in orthogonal polynomials. It is based on the use of maximum likelihood estimates for the coefficients in the expansion, together with the use of the AIC stopping rule to determine the number of coefficients included. Examples are given of estimating Poisson densities in 1-(time), 2-(space) and 3-(space-time) dimensions. A procedure for discussing space-time independence is described. Extensions are discussed for estimating first order densities in certain types of non-homogeneous cluster processes. (ERA citation 12:008798)