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Consistency in systematic sampling

Part of: Global differential geometry Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

X. Gual Arnau  and
L. M. Cruz-Orive
X. Gual Arnau*
Affiliation:
Universitat Jaume I
L. M. Cruz-Orive*
Affiliation:
Universidad de Cantabria and Universität Bern
*
∗ Postal address: Departament de Matemàtiques, Penyeta Roja, Universitat Jaume I, E-12071 Castellón, Spain.
∗∗ Postal address: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. Los Castros, E-39005 Santander, Spain.
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Abstract

In design-based stereology, fixed parameters (such as volume, surface area, curve length, feature number, connectivity) of a non-random geometrical object are estimated by intersecting the object with randomly located and oriented geometrical probes (e.g. test slabs, planes, lines, points). Estimation accuracy may in principle be increased by increasing the number of probes, which are usually laid in a systematic pattern. An important prerequisite to increase accuracy, however, is that the relevant estimators are unbiased and consistent. The purpose of this paper is therefore to give sufficient conditions for the unbiasedness and strong consistency of design-based stereological estimators obtained by systematic sampling. Relevant mechanisms to increase sample size, compatible with stereological practice, are considered.

Keywords

CONSISTENCYDESIGN BASED INFERENCELATTICE RETRACTMODEL BASED INFERENCESTEREOLOGYSYSTEMATIC SAMPLINGTEST SYSTEMUNBIASEDNESS

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 53C65: Integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 4 , December 1996 , pp. 982 - 992
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Work supported by the Swiss National Science Foundation Grant #31-28610.90, Dirección General de Investigación Científica y Técnica Grant #PB94-1058 and Fundació Caixa Castelló Grant #P1A-94-24.

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