On the asymptotic efficiency of estimators

Teresa Ledwina. "On the asymptotic efficiency of estimators." Mathematica Applicanda 35.49/08 (2007): null. <http://eudml.org/doc/293032>.

@article{TeresaLedwina2007,
abstract = {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.},
author = {Teresa Ledwina},
journal = {Mathematica Applicanda},
keywords = {Asymptotic efficiency, Asymptotic optimality, Influence function, Superefficiency, Score test.},
language = {eng},
number = {49/08},
pages = {null},
title = {On the asymptotic efficiency of estimators},
url = {http://eudml.org/doc/293032},
volume = {35},
year = {2007},
}

TY - JOUR
AU - Teresa Ledwina
TI - On the asymptotic efficiency of estimators
JO - Mathematica Applicanda
PY - 2007
VL - 35
IS - 49/08
SP - null
AB - 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.
LA - eng
KW - Asymptotic efficiency, Asymptotic optimality, Influence function, Superefficiency, Score test.
UR - http://eudml.org/doc/293032
ER -