## The Annals of Statistics

### Maximizing the Variance of $M$-Estimators Using the Generalized Method of Moment Spaces

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 567-577.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345460

Digital Object Identifier
doi:10.1214/aos/1176345460

Mathematical Reviews number (MathSciNet)
MR615432

Zentralblatt MATH identifier
0479.62026

JSTOR
Collins, John R.; Portnoy, Stephen L. Maximizing the Variance of $M$-Estimators Using the Generalized Method of Moment Spaces. Ann. Statist. 9 (1981), no. 3, 567--577. doi:10.1214/aos/1176345460. https://projecteuclid.org/euclid.aos/1176345460