Results of an earlier paper giving first order optimal robust $M$-estimators of a location parameter in certain dependent situations are extended to the case where the dependency can be modeled by a symmetric form of a $(2k + 1)$st order moving average scheme. It is also shown that the results can not be extended to finding second order optimal $M$-estimators. That is, no $M$-estimators can be optimal to the second order unless they explicitly adapt themselves to the assumed model for dependency.
Publié le : 1979-01-14
Classification:
Robust estimation,
dependent observations,
approximate asymptotic optimality over $\arepsilon$-contaminated normals,
62G35,
62F10
@article{1176344568,
author = {Portnoy, Stephen L.},
title = {Further Remarks on Robust Estimation in Dependent Situations},
journal = {Ann. Statist.},
volume = {7},
number = {1},
year = {1979},
pages = { 224-231},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344568}
}
Portnoy, Stephen L. Further Remarks on Robust Estimation in Dependent Situations. Ann. Statist., Tome 7 (1979) no. 1, pp. 224-231. http://gdmltest.u-ga.fr/item/1176344568/