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A note on design-based versus model-based variance estimation in stereology

Part of: General convexity Global differential geometry Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Asger Hobolth  and
Eva B. Vedel Jensen
Asger Hobolth*
Affiliation:
University of Aarhus
Eva B. Vedel Jensen*
Affiliation:
University of Aarhus
*
∗ Postal address: Laboratory for Computational Stochastics, Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark.
∗ Postal address: Laboratory for Computational Stochastics, Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark.
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Abstract

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

Keywords

Covariogramcirculant matrixFourier seriesplanar objectsshapestationaritystereologysystematic sampling

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry 53C65: Integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 34 , Issue 3 , September 2002 , pp. 484 - 490
Copyright
Copyright © Applied Probability Trust 2002 

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References

Abramovitz, M. and Stegun, I. A. (1965). Handbook of Mathematical Functions. Dover, New York.Google Scholar
Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998). Model-based geostatistics (with discussion). Appl. Statist. 47, 299–350.Google Scholar
Gual-Arnau, X. and Cruz-Orive, L. M. (2000). Systematic sampling on the circle and on the sphere. Adv. Appl. Prob. 32, 628–647.Google Scholar
Hobolth, A., Kent, J. T. and Dryden, I. L. (2002). On the relation between edge and vertex modelling in shape analysis. To appear in Scand. J. Statist.Google Scholar
Hobolth, A., Pedersen, J. and Jensen, E. B. V. (2002). A continuous parametric shape model. To appear in Ann. Inst. Statist. Math.Google Scholar
Stein, M. L. (1999). Interpolation of Spatial Data. Springer, New York.Google Scholar
Wahba, G. (1990). Spline Models for Observational Data (CBMS-NSF Regional Conf. Ser. Appl. Math. 59). SIAM, Philadelpia, PA.Google Scholar
Wei, W. W. S. (1990). Time Series Analysis. Addison-Wesley, Redwood City, CA.Google Scholar