Nonparametric estimators of probability characteristics using unbiased prior conditions

Yury G. Dmitriev () and Gennady M. Koshkin
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Yury G. Dmitriev: National Research Tomsk State University
Gennady M. Koshkin: National Research Tomsk State University

Statistical Papers, 2018, vol. 59, issue 4, No 18, 1559-1575

Abstract: 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.

Keywords: Nonparametric estimator; Auxiliary information; U-statistics; Mises functional; Asymptotic normality (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00362-018-1044-7

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