The problem considered is that of optimizing a function of a finite number of linear functionals over an infinite dimensional convex set $S$. It is shown that under some reasonably general conditions the method of moment spaces can be used to reduce the problem to one of optimizing over a simple finite dimensional set (generally a set of convex combinations of extreme points of $S$). The results are applied to finding the maximum asymptotic variance of M-estimators over classes of distributions arising in the theory of robust estimation.
Publié le : 1981-05-14
Classification:
Method of moment spaces,
robust estimation,
asymptotic variance,
62G35,
62G05
@article{1176345460,
author = {Collins, John R. and Portnoy, Stephen L.},
title = {Maximizing the Variance of $M$-Estimators Using the Generalized Method of Moment Spaces},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 567-577},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345460}
}
Collins, John R.; Portnoy, Stephen L. Maximizing the Variance of $M$-Estimators Using the Generalized Method of Moment Spaces. Ann. Statist., Tome 9 (1981) no. 1, pp. 567-577. http://gdmltest.u-ga.fr/item/1176345460/