Geodesic
On the asymptotic efficiency of estimators
Mathematica Applicanda, Tome 35 (2007) no. 49/08, pp. 66-83.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

We present and discuss the notion of asymptotic efficiency of estimators as introduced by Hajek and Le Cam. We give also some general construction of a class of asymptotically efficient estimators of Euclidean parameters. Moreover, we briefly indicate some generalizations of the discussed ideas to the case of semiparametric models. We show also that technical results obtained in the asymptotic theory of efficient estimation can be successfully used in asymptotic theory of testing. The selection of the material is highly subjective and to a little extent reflects complexity of several problems and range of results available in present-day literature. The paper is a shortened version of invited series of lectures presented at the Conference on Mathematical Statistics WISŁA 2005. Its main purpose is to show that classic approach to define efficiency was not satisfactory and to discuss how, for some class of problems, this question was solved in a natural and elegant way.
DOI : 10.14708/ma.v35i49/08.1388
Classification : 62G20 (62F10)
Mots-clés : Asymptotic efficiency, Asymptotic optimality, Influence function, Superefficiency, Score test. 
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Teresa Ledwina. On the asymptotic efficiency of estimators. Mathematica Applicanda, Tome 35 (2007) no. 49/08, pp.  66-83. doi : 10.14708/ma.v35i49/08.1388. http://geodesic.mathdoc.fr/articles/10.14708/ma.v35i49/08.1388/

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