Abstract
For estimation of functions involving only parameters of interest, in the presence of nuisance parameters, some optimality properties are established for partially sufficient (i.e. p-sufficient) statistics in two classes of regular probability models. The results are based on a characterization of regular unbiased estimating functions for parameters of interest in probability models for which a statistic exists such that its marginal distribution depends on unknown parameters only through the parameters of interest.
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Bhapkar, V.P. On the Optimality of Estimators Based on P-Sufficient Statistics. Annals of the Institute of Statistical Mathematics 52, 173–183 (2000). https://doi.org/10.1023/A:1004149318827
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DOI: https://doi.org/10.1023/A:1004149318827