THE RAO-BLACKWELL THEOREM IN STEREOLOGY AND SOME COUNTEREXAMPLES

被引:18
作者
BADDELEY, AJ [1 ]
CRUZORIVE, LM [1 ]
机构
[1] UNIV BERN,BERN,SWITZERLAND
关键词
CARTIERS FORMULA; COMPLETE SIGMA-ALGEBRA; COVARIANCE FUNCTION; EFFICIENT ESTIMATION; GEOSTATISTICS; GRENANDERS THEOREM; POINT COUNTING; QUADRAT SAMPLING; RANDOM CLOSED SETS; RANDOMIZED SUBSAMPLING; SMITS PARADOX; SPATIAL SAMPLING DESIGN; SPATIAL STATISTICS; STOCHASTIC GEOMETRY; SUFFICIENT SIGMA-ALGEBRA; TEST SYSTEMS; WIDE-SENSE STATIONARY RANDOM FIELDS;
D O I
10.2307/1428091
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:2 / 19
页数:18
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