Publication at Faculty of Mathematics and Physics |
2010
Abstract
We investigate a class of kernel estimators of the asymptotic variance of a d-dimensional stationary point process which can be observed in a cubic sampling window. Depending on the rate of decay (polynomially or exponentially) of the total variation of reduced second order factorial moment measure outside of an expanding ball centered at the origin, we determine optimal bandwidths minimizing the mean squared error of the asymptotic variance.
Our theoretical results are illustrated and supported by a simulation study which compares the (relative) mean squared errors of the estimator of asymptotic variance for planar Poisson, Poisson cluster, and hard-core point processes and for various values of the bandwidth.