Central limit theorems for functionals of stationary germ-grain models

Abstract

Conditions are derived for the asymptotic normality of a general class of vector-valued functionals of stationary Boolean models in the d-dimensional Euclidean space, where a Lindeberg-type central limit theorem for m-dependent random fields, m ∈ N, is applied. These functionals can be used to construct joint estimators for the vector of specific intrinsic volumes of the underlying Boolean model. Extensions to functionals of more general germ-grain models satisfying some mixing and integrability conditions are also discussed.

Central limit theorems for Poisson hyperplane tessellations

“…In [19] (and references therein), the reader can find a lot of further CLTs for empirical characteristics of Boolean models. Consistency properties and asymptotic normality of joint estimators for the whole vector of specific intrinsic volumes of stationary random sets in R d have been derived in [23] and [28], while uniformly best unbiased estimators for the intensity of stationary flat processes have been considered in [27].…”