Skip to main content Accessibility help
×
Home

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

  • Asger Hobolth (a1) and Eva B. Vedel Jensen (a1)

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.

Copyright

Corresponding author

Postal address: Laboratory for Computational Stochastics, Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark.
∗∗ Email address: asho@imf.au.dk

References

Hide All
Abramovitz, M. and Stegun, I. A. (1965). Handbook of Mathematical Functions. Dover, New York.
Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998). Model-based geostatistics (with discussion). Appl. Statist. 47, 299350.
Gual-Arnau, X. and Cruz-Orive, L. M. (2000). Systematic sampling on the circle and on the sphere. Adv. Appl. Prob. 32, 628647.
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.
Hobolth, A., Pedersen, J. and Jensen, E. B. V. (2002). A continuous parametric shape model. To appear in Ann. Inst. Statist. Math.
Stein, M. L. (1999). Interpolation of Spatial Data. Springer, New York.
Wahba, G. (1990). Spline Models for Observational Data (CBMS-NSF Regional Conf. Ser. Appl. Math. 59). SIAM, Philadelpia, PA.
Wei, W. W. S. (1990). Time Series Analysis. Addison-Wesley, Redwood City, CA.

Keywords

MSC classification

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

  • Asger Hobolth (a1) and Eva B. Vedel Jensen (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed