## The Annals of Statistics

### Efficiency Versus Robustness: The Case for Minimum Hellinger Distance and Related Methods

Bruce G. Lindsay

#### Abstract

It is shown how and why the influence curve poorly measures the robustness properties of minimum Hellinger distance estimation. Rather, for this and related forms of estimation, there is another function, the residual adjustment function, that carries the relevant information about the trade-off between efficiency and robustness. It is demonstrated that this function determines various second-order measures of efficiency and robustness through a scalar measure called the estimation curvature. The function is also shown to determine the breakdown properties of the estimators through its tail behavior. A 50% breakdown result is given. It is shown how to create flexible classes of estimation methods in the spirit of $M$-estimation, but with first-order efficiency (or even second-order efficiency) at the chosen model, 50% breakdown and a minimum distance interpretation.

#### Article information

Source
Ann. Statist., Volume 22, Number 2 (1994), 1081-1114.

Dates
First available in Project Euclid: 11 April 2007

https://projecteuclid.org/euclid.aos/1176325512

Digital Object Identifier
doi:10.1214/aos/1176325512

Mathematical Reviews number (MathSciNet)
MR1292557

Zentralblatt MATH identifier
0807.62030

JSTOR