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Nonparametric estimators of probability characteristics using unbiased prior conditions

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Abstract

A class of nonparametric estimators of the main functional of distribution constructed by making use auxiliary information is proposed. It is shown that the knowledge usage of other distribution functionals in estimation of the main functional can often provide the mean squared error (MSE) smaller than that of estimators constructed without such auxiliary information. In the paper, the adaptive estimators are proposed. The asymptotic normality of all the proposed estimators is proved. The simulation results show that the usage of auxiliary information in estimation procedure improves the MSE of estimators.

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Authors and Affiliations

  1. National Research Tomsk State University, Tomsk, Russia

    Yury G. Dmitriev & Gennady M. Koshkin

Authors
  1. Yury G. Dmitriev
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  2. Gennady M. Koshkin
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Correspondence to Yury G. Dmitriev.

Additional information

This research was supported by “The Tomsk State University competitiveness improvement programme” under Grant No. 8.1.37.2018.

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Dmitriev, Y.G., Koshkin, G.M. Nonparametric estimators of probability characteristics using unbiased prior conditions. Stat Papers 59, 1559–1575 (2018). https://doi.org/10.1007/s00362-018-1044-7

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  • DOI: https://doi.org/10.1007/s00362-018-1044-7

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