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A rate of convergence for the set compound estimation in a family of certain retracted distributions

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Summary

This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate\(\hat G_n \) of the empiric distributionG n of the parameters θ1,...,θn for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on\(\hat G_n \) with a convergence rateO((n −1 logn)1/4) for the mofified regret uniformly in (θ1, θ2, ..., θn ∈ Ωn with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞).

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Authors and Affiliations

  1. The University of Tsukuba, Tsukuba, Japan

    Yoshiko Nogami

Authors
  1. Yoshiko Nogami
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Additional information

This is part of the author's Ph. D. Thesis at Michigan State University.

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Nogami, Y. A rate of convergence for the set compound estimation in a family of certain retracted distributions. Ann Inst Stat Math 34, 241–257 (1982). https://doi.org/10.1007/BF02481025

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  • DOI: https://doi.org/10.1007/BF02481025

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