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A truncated estimation method with guaranteed accuracy

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Abstract

This paper presents a truncated estimation method of ratio type functionals by dependent sample of finite size. This method makes it possible to obtain estimators with guaranteed accuracy in the sense of the \(L_m\)-norm, \(m\ge 2\). As an illustration, the parametric and non-parametric estimation problems on a time interval of a fixed length are considered. In particular, parameters of linear (autoregressive) and non-linear discrete-time processes are estimated. Moreover, the parameter estimation problem of non-Gaussian Ornstein-Uhlenbeck process by discrete-time observations and the estimation problem of a multivariate logarithmic derivative of a noise density of an autoregressive process with guaranteed accuracy are solved. In addition to non-asymptotic properties, the limit behavior of presented estimators is investigated. It is shown that all the truncated estimators have asymptotic properties of basic estimators. In particular, the asymptotic efficiency in the mean square sense of the truncated estimator of the dynamic parameter of a stable autoregressive process is established.

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Acknowledgments

The author is grateful to the anonymous reviewer, as well as to the editor and an associated editor for constructive criticism and clear guidelines. Finally, the author thanks S. Pergamenshchikov for the helpful comments and discussion on (12).

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Authors and Affiliations

  1. Department of Applied Mathematics and Cybernetics, Tomsk State University, Lenina 36, 634050 , Tomsk, Russia

    Vyacheslav A. Vasiliev

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  1. Vyacheslav A. Vasiliev
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Correspondence to Vyacheslav A. Vasiliev.

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Vasiliev, V.A. A truncated estimation method with guaranteed accuracy. Ann Inst Stat Math 66, 141–163 (2014). https://doi.org/10.1007/s10463-013-0409-x

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  • DOI: https://doi.org/10.1007/s10463-013-0409-x

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