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Unbiased estimators in the sense of Lehmann and their discrimination rates

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Summary

In this paper, we define the index of performance of unbiased estimators in the sense of Lehmann (L-unbiased), which evaluates the power for the estimators to discriminate any wrong values of a parametric function from a correct one. We shall call the indexdiscrimination rate of the estimator. The larger discrimination rate the estimator has, the more desirable it is. An upper bound of discrimination rates is obtained, which is given by thesensitivity of the probability family under consideration. The discrimination rates of several L-unbiased estimators are investigated. Moreover we discuss the conditions under which the L-unbiased estimator is improved in the sense of discrimination rate by the L-unbiased estimator depending only on a sufficient statistic.

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Authors
  1. Hisataka Kuboki
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Additional information

This research was supported in part by a Grant-in-Aid for Scientific Research of the Japanese Ministry of Education, Science and Culture.

The Institute of Statistical Mathematics

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Kuboki, H. Unbiased estimators in the sense of Lehmann and their discrimination rates. Ann Inst Stat Math 34, 19–37 (1982). https://doi.org/10.1007/BF02481005

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  • DOI: https://doi.org/10.1007/BF02481005

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