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Asymptotically optimal estimators for moments of change

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Ukrainian Mathematical Journal Aims and scope

Abstract

We consider the problem of finding asymptotically optimal estimators for many moments of change in the case of incomplete information on distributions. We prove that if the maximum-likelihood estimator is asymptotically optimal, then, under certain conditions, it preserves this property after the replacement of actual values by density estimators. We solve the problem for the case of one moment of change and generalize the results obtained to the case of several moments of change.

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv

    H. V. Shurenkov

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  1. H. V. Shurenkov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 3, pp. 406–416, March, 2006.

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Shurenkov, H.V. Asymptotically optimal estimators for moments of change. Ukr Math J 58, 458–471 (2006). https://doi.org/10.1007/s11253-006-0078-5

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  • DOI: https://doi.org/10.1007/s11253-006-0078-5

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