Open AccessImproving the Cavalieri estimator under non-equidistant sampling and dropouts
Author(s) -
Mads Stehr,
Markus Kiderlen
Publication year - 2020
Publication title -
image analysis and stereology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.237
H-Index - 27
eISSN - 1854-5165
pISSN - 1580-3139
DOI - 10.5566/ias.2422
Subject(s) - equidistant , estimator , mathematics , sampling (signal processing) , variance (accounting) , minimum variance unbiased estimator , bounded function , regular polygon , statistics , geometry , mathematical analysis , computer science , accounting , filter (signal processing) , business , computer vision
Motivated by the stereological problem of volume estimation from parallel section profiles, the so-called Newton-Cotes integral estimators based on random sampling nodes are analyzed. These estimators generalize the classical Cavalieri estimator and its variant for non-equidistant sampling nodes, the generalized Cavalieri estimator, and have typically a substantially smaller variance than the latter. The present paper focuses on the following points in relation to Newton-Cotes estimators: the treatment of dropouts, the construction of variance estimators, and, finally, their application in volume estimation of convex bodies.Dropouts are eliminated points in the initial stationary point process of sampling nodes, modeled by independent thinning. Among other things, exact representations of the variance are given in terms of the thinning probability and increments of the initial points under two practically relevant sampling models. The paper presents a general estimation procedure for the variance of Newton-Cotes estimators based on the sampling nodes in a bounded interval. Finally, the findings are illustrated in an application of volume estimation for three-dimensional convex bodies with sufficiently smooth boundaries.