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Consistency in systematic sampling for stereology

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
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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), [4], [5], [8], [11], [12]. Estimation accuracy may in principle be increased by increasing the number of probes, which are usually laid in a systematic pattern, [1], [2], [3], [7], [9], [10]. An important prerequisite to increase accuracy, however, is that the relevant estimators are unbiased and consistent. Our purpose is therefore to give sufficient conditions for the unbiasedness and strong consistency of design-based stereological estimators obtained by systematic sampling.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 329 - 330
Copyright
Copyright © Applied Probability Trust 1996 

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References

[1] Cruz-Orive, L. M. (1982) The use of quadrats and test systems in stereology, including magnification corrections.p J. Microsc. 125, 89–102.Google Scholar
[2] Cruz-Orive, L. M. (1989) On the precision of systematic sampling: a review of Matheron's transitive methods. J. Microsc. 153, 315–333.CrossRefGoogle Scholar
[3] Cruz-Orive, L. M. (1993) Systematic sampling in stereology. Bullet. Int. Statist. Inst., Proc. 49th Session, Florence 1993, 52, 451–468.Google Scholar
[4] Cruz-Orive, L. M. and Weibel, Ε. R. (1990) Recent stereological methods for cell biology: a brief survey. Amer. J. Physiol. 258, L148–L156.Google ScholarPubMed
[5] Davy, P. J. and Miles, R. E. (1977) Sampling theory for opaque spatial specimens. J. R. Statist. Soc. B 39, 56–65.Google Scholar
[6] Gual Arnau, X. and Cruz-Orive, L. M. (1996) Consistency in systematic sampling. (Submitted for publication.)Google Scholar
[7] Gundersen, H. J. G. and Jensen, Ε. B. (1987) The efficiency of systematic sampling in stereology and its prediction. J. Microsc. 147, 229–263.CrossRefGoogle ScholarPubMed
[8] Jensen, E. B., Baddeley, A. J., Gundersen, H. J. G. and Sundberg, R. (1985) Recent trends in stereology. Int. Statist. Rev. 53, 99–108.CrossRefGoogle Scholar
[9] Miles, R. E. and Davy, P. J. (1977) On the choice of quadrats in stereology. J. Microsc. 110, 27–44.Google Scholar
[10] Santaló, L. A., (1976) Integral Geometry and Geometric Probability. Addison-Wesley, Reading, MA.Google Scholar
[11] Stoyan, D., Kendall, W. S. and Mecke, J. (1987) Stochastic Geometry and its Applications. Wiley, Chichester.Google Scholar
[12] Weibel, Ε. R., (1980) Stereological Methods. Vol. 2: Theoretical Foundations. Academic Press, London.Google Scholar