BAYESIAN SELECTION OF LOCAL BANDWIDTH IN NON-HOMOGENEOUS POISSON PROCESS KERNEL ESTIMATORS FOR THE INTENSITY FUNCTION

摘要

In this paper, the proposed estimator for the bivariate intensity function for non-homogeneous Poisson process is based on multivariate continuous associated kernels. It is well known that, the serious problem inherent in this approach is that performance of the kernel estimator depends on the selection of a bandwidth parameter. To overcome the problem, we propose a Bayesian local approach to select the matrix of bandwidths considering the bivariate intensity function, and treating the bandwidths as a diagonal matrix of parameters with some prior distribution. To get an optimum parameter we have considered the selection of the local Bayesian bandwidth, which will then be compared, in terms of performance, to other approaches such as cross-validation method, Scott’s rule of thumbs, respectively. Note that the proposed method, in comparison in terms of minimizing the asymptotic mean integrated squared error, turn out favourably for the Bayesian method in examples studied.