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On Risks of Estimates Based on Random-Size Samples

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Abstract

An asymptotical approach to the statistical estimation problem is considered under the assumption that the number of observations is a random variable. This leads to distributions with heavy tails and changes in the efficiency of the normally used statistical procedures. Statistical estimates based on random-size and nonrandom-size samples are asymptotically compared against one another. The concept of asymptotic deficiency (the number of additional observations needed for a given estimate to achieve the same quality as the optimum estimate) is used to do so. Asymptotic expansions are also obtained for the risk functions of estimates based on random-size samples.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-07-00252.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    V. E. Bening

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  1. V. E. Bening
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Correspondence to V. E. Bening.

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Translated by A. Muravnik

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Bening, V.E. On Risks of Estimates Based on Random-Size Samples. MoscowUniv.Comput.Math.Cybern. 44, 16–26 (2020). https://doi.org/10.3103/S0278641920010045

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