A COMPARISON OF NONPARAMETRIC ESTIMATORS FOR LENGTH DISTRIBUTION IN LINE SEGMENT PROCESSES

Image Analysis and Stereology

Marketa Zikmundova¹  Zbynek Pawlas² 

[1] Department of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology, Prague;Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University;

关键词: Horvitz-Thompson estimator;    Kaplan-Meier estimator;    line segment process;    nonparametric maximum likelihood estimator;    reduced-sample estimator;    SRE algorithm;   

DOI  :  10.5566/ias.1889

来源: DOAJ

【 摘 要 】

We study nonparametric estimation of the length distribution for stationary line segment processes in the d-dimensional Euclidean space. Several methods have been proposed in the literature. We review different approaches (Horvitz-Thompson type estimator, reduced-sample estimator, Kaplan-Meier estimator, nonparametric maximum likelihood estimator, stochastic restoration estimation) and compare the finite sample behaviour by means of a simulation study for stationary line segment processes in 2D and 3D. Several data generating processes (Poisson point process, Matérn cluster process and Matérn hard-core process II) are considered with both independent and dependent segments. Our finite sample comparison reveals that the nonparametric likelihood estimator provides the most preferable method which works reasonably also if its assumptions are not satisfied.

【 授权许可】

Unknown