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Limiting experiments and asymptotic bounds on the performance of sequence of estimators. (English) Zbl 1383.62022
Ferger, Dietmar (ed.) et al., From statistics to mathematical finance. Festschrift in honour of Winfried Stute. Cham: Springer (ISBN 978-3-319-50985-3/hbk; 978-3-319-50986-0/ebook). 317-342 (2017).
Summary: 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.
For the entire collection see [Zbl 1383.62010].
MSC:
62B15 Theory of statistical experiments
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