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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2001-31
October 2001

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


Eva B. Vedel Jensen

Asger Hobolth


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 in Hobolth et al. (1999, 2000) 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.

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This paper has now been published in Adv. in Appl. Probab. 34, 484--490 (2002)