This paper defines and studies for independent identically distributed observations a new parametric estimation procedure which is asymptotically efficient under a specified regular parametric family of densities and is minimax robust in a small Hellinger metric neighborhood of the given family. Associated with the estimator is a goodness-of-fit statistic which assesses the adequacy of the chosen parametric model. The fitting of a normal location-scale model by the new procedure is exhibited numerically on clear and on contaminated data.
@article{1176343842,
author = {Beran, Rudolf},
title = {Minimum Hellinger Distance Estimates for Parametric Models},
journal = {Ann. Statist.},
volume = {5},
number = {1},
year = {1977},
pages = { 445-463},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343842}
}
Beran, Rudolf. Minimum Hellinger Distance Estimates for Parametric Models. Ann. Statist., Tome 5 (1977) no. 1, pp. 445-463. http://gdmltest.u-ga.fr/item/1176343842/