The Rao-Blackwell theorem in stereology and some counterexamples

Adrian Baddeley, L.M. Cruz-Orive

    Research output: Contribution to journalArticle

    Abstract

    A version of the Rao-Blackwell theorem is shown to apply to most, but not all, stereological sampling designs. Estimators based on random test grids typically have larger variance than quadrat estimators; random s-dimensional samples are worse than random r-dimensional samples for s <r. Furthermore, the standard stereological ratio estimators of different dimensions are canonically related to each other by the Rao-Blackwell process. However, there are realistic cases where sampling with a lower-dimensional probe increases efficiency. For example, estimators based on (conditionally) non-randomised test point grids may have smaller variance than quadrat estimators. Relative efficiency is related to issues in geostatistics and the theory of wide-sense stationary random fields. A uniform minimum variance unbiased estimator typically does not exist in our context.
    Original languageEnglish
    Pages (from-to)2-19
    JournalAdvances in Applied Probability
    Volume27
    DOIs
    Publication statusPublished - 1995

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