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From Statistics to Mathematical Finance pp 317–342Cite as

Limiting Experiments and Asymptotic Bounds on the Performance of Sequence of Estimators

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Abstract

In this paper, we provide a review of rather selected results among those available in the literature on asymptotic theory of statistical inference. We do not claim an exhaustive review of the relative literature, which, at any rate, could hardly be achieved in the limited space provided for a contributing paper. Instead, we focus mainly on references leading or closely related to our own research results. The discussion encompasses the concepts of limit experiments and asymptotic bounds on the performance of sequences of estimators. The concepts and methodology used are those of contiguity (defined in Definition 1), local asymptotic normality (LAN), local asymptotic mixed normality (LAMN), local asymptotic quadratic (LAQ) (all defined after relations (16.3b) and (16.4) in the paper), and local asymptotic minimax risk of a sequence of estimators.

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Acknowledgements

An early draft of the paper was carefully reviewed by two referees. They made some useful comments and suggestions on the inclusion of additional references, which were adopted and implemented in this version of the paper, and they are gratefully acknowledged herewith.

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Authors and Affiliations

  1. Visva-Bharati University, Santiniketan, India

    Debasis Bhattacharya

  2. University of California, Davis, California, USA

    George G. Roussas

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  1. Debasis Bhattacharya
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Correspondence to Debasis Bhattacharya .

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Editors and Affiliations

  1. Institute of Mathematical Stochastics, Technische Universität Dresden, Dresden, Germany

    Dietmar Ferger

  2. Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain

    Wenceslao González Manteiga

  3. Institute of Mathematics, University of Freiburg, Freiburg, Germany

    Thorsten Schmidt

  4. Department of Statistics, University of California, Davis, California, USA

    Jane-Ling Wang

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Bhattacharya, D., Roussas, G.G. (2017). Limiting Experiments and Asymptotic Bounds on the Performance of Sequence of Estimators. In: Ferger, D., González Manteiga, W., Schmidt, T., Wang, JL. (eds) From Statistics to Mathematical Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-50986-0_16

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