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Precision of circular systematic sampling
Author(s) -
CruzOrive L. M.,
GualArnau X.
Publication year - 2002
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1046/j.1365-2818.2002.01057.x
Subject(s) - sampling (signal processing) , estimator , systematic sampling , sample (material) , planar , mathematics , systematic error , isotropy , object (grammar) , statistics , stereology , sample size determination , surface (topology) , orientation (vector space) , algorithm , geometry , computer science , artificial intelligence , physics , optics , biology , computer graphics (images) , filter (signal processing) , computer vision , thermodynamics , endocrinology
Summary In design stereology, many estimators require isotropic orientation of a test probe relative to the object in order to attain unbiasedness. In such cases, systematic sampling of orientations becomes imperative on grounds of efficiency and practical applicability. For instance, the planar nucleator and the vertical rotator imply systematic sampling on the circle, whereas the Buffon–Steinhaus method to estimate curve length in the plane, or the vertical designs to estimate surface area and curve length, imply systematic sampling on the semicircle. This leads to the need for predicting the precision of systematic sampling on the circle and the semicircle from a single sample. There are two main prediction approaches, namely the classical one of G. Matheron for non‐necessarily periodic measurement functions, and a recent approach based on a global symmetric model of the covariogram, more specific for periodic measurement functions. The latter approach seems at least as satisfactory as the former for small sample sizes, and it is developed here incorporating local errors. Detailed examples illustrating common stereological tools are included.