The finite-sample breakdown points and finite-sample tail behavior are studied for a class of equivariant estimators in the linear regression model under a fixed design. The same is considered for the one-step and -step versions of the estimators, starting with an initial estimator. It is shown that the tail-behavior of the one- and -step versions of an estimator is determined mainly by that of the initial estimator.
Les points de rupture et le comportement des queues sous des échantillons finis sont etudiés pour une classe d’estimateurs equivariants dans le modèle linéaire avec un design fixe. Des résultats du même type sont obtenus pour des itérations de type Newton-Raphson d’un estimateur initial. On démontre que le comportement des queues de ces estimateurs itérés est principalemnt déterminé par celui de l’estimateur initial.
Keywords: point de rupture, estimateur equivariant, comportement des queues
@article{JSFS_2012__153_1_44_0, author = {Jure\v{c}kov\'a, Jana}, title = {Tail-behavior of estimators and of their one-step versions}, journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique}, pages = {44--51}, publisher = {Soci\'et\'e fran\c{c}aise de statistique}, volume = {153}, number = {1}, year = {2012}, mrnumber = {2930289}, zbl = {1316.62099}, language = {en}, url = {http://archive.numdam.org/item/JSFS_2012__153_1_44_0/} }
TY - JOUR AU - Jurečková, Jana TI - Tail-behavior of estimators and of their one-step versions JO - Journal de la société française de statistique PY - 2012 SP - 44 EP - 51 VL - 153 IS - 1 PB - Société française de statistique UR - http://archive.numdam.org/item/JSFS_2012__153_1_44_0/ LA - en ID - JSFS_2012__153_1_44_0 ER -
%0 Journal Article %A Jurečková, Jana %T Tail-behavior of estimators and of their one-step versions %J Journal de la société française de statistique %D 2012 %P 44-51 %V 153 %N 1 %I Société française de statistique %U http://archive.numdam.org/item/JSFS_2012__153_1_44_0/ %G en %F JSFS_2012__153_1_44_0
Jurečková, Jana. Tail-behavior of estimators and of their one-step versions. Journal de la société française de statistique, Volume 153 (2012) no. 1, pp. 44-51. http://archive.numdam.org/item/JSFS_2012__153_1_44_0/
[1] Tail behavior of regression estimators and their breakdown points, Econometrica, Volume 58 ((1990)), pp. 1195-1214 | MR | Zbl
[2] The asymptotics for studentized k-step M-estimators of location, Sequential Analysis, Volume 14 ((1995)), pp. 229-245 | MR | Zbl
[3] Minimum risk equivariant estimators in linear regression model, Statistics & Decisions, Volume 27 ((2009)), pp. 37-59 | MR | Zbl
[4] Finite-sample behavior of robust estimators, Recent Researches in Instrumentation, Measurement, Circuits and Systems (et al., S. Chen, ed.), WSEAS, ISSN 1792-8575, (2011), pp. 15-20
[5] Asymptotics for one-step M-estimators in regression with application to combining efficiency and high breakdown point, Commun. Statist. A, Volume 16 ((1987)), pp. 2187-2199 | MR | Zbl
[6] Effect of the initial estimator on the asymptotic behavior of one-step M-estimator, Ann. Inst. Statist. Math., Volume 42 ((1990)), pp. 345-357 | MR | Zbl
[7] Tail behavior of location estimators, Ann. Statist., Volume 9 ((1981)), pp. 578-585 | MR | Zbl
[8] Breakdown points and variation exponents of robust M-estimators in linear models, Ann. Statist, Volume 27 ((1999)), pp. 1164-1177 | MR | Zbl