## The Annals of Mathematical Statistics

### A General Qualitative Definition of Robustness

Frank R. Hampel

#### Abstract

Two very closely related definitions of robustness of a sequence of estimators are given which take into account the types of deviations from parametric models that occur in practice. These definitions utilize the properties of the Prokhorov distance between probability distributions. It is proved that weak $^\ast$-continuous functionals on the space of probability distributions define robust sequences of estimators (in either sense). The concept of the "breakdown point" of a sequence of estimators is defined, and some examples are given.

#### Article information

Source
Ann. Math. Statist., Volume 42, Number 6 (1971), 1887-1896.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177693054

Digital Object Identifier
doi:10.1214/aoms/1177693054

Mathematical Reviews number (MathSciNet)
MR301858

Zentralblatt MATH identifier
0229.62041

JSTOR
links.jstor.org

#### Citation

Hampel, Frank R. A General Qualitative Definition of Robustness. Ann. Math. Statist. 42 (1971), no. 6, 1887--1896. doi:10.1214/aoms/1177693054. https://projecteuclid.org/euclid.aoms/1177693054