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

In: From Statistics to Mathematical Finance

Author

Listed:
  • Debasis Bhattacharya

    (Visva-Bharati University)

  • George G. Roussas

    (University of California)

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.

Suggested Citation

  • Debasis Bhattacharya & George G. Roussas, 2017. "Limiting Experiments and Asymptotic Bounds on the Performance of Sequence of Estimators," Springer Books, in: Dietmar Ferger & Wenceslao González Manteiga & Thorsten Schmidt & Jane-Ling Wang (ed.), From Statistics to Mathematical Finance, chapter 0, pages 317-342, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-50986-0_16
    DOI: 10.1007/978-3-319-50986-0_16
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