Joint estimators for the specific intrinsic volumes of stationary random sets

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:115

Article

Schmidt, V ; Spodarev, E

关键词: stochastic geometry;    random closed set;    volume fraction;    specific surface area;    Euler-Poincare characteristic;    stationary random field;    nonparametric estimation;    unbiasedness;    consistency;    asymptotic normality;   

DOI  :  10.1016/j.spa.2004.12.007

来源: Elsevier

【 摘 要 】

Stationary random closed sets Xi in R-d are considered whose realizations belong to the extended convex ring. A new approach is proposed to joint estimation of the specific intrinsic volumes (V) over bar (0)(Xi), ..., (V) over bar (d)(Xi) of Xi, including the specific Euler-Poincare characteristic (V) over bar (0)(Xi), the specific surface area 2 (V) over bar (d-1)(Xi), and the volume fraction (V) over bard(Xi) of Xi. Nonparametric estimators are constructed, which can be represented by integrals of some stationary random fields. This implies in particular that these estimators are unbiased. Moreover, conditions are derived which ensure that they are mean-square consistent. A consistent estimator for their asymptotic covariance matrix is derived. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

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