## The Annals of Mathematical Statistics

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

### A General Qualitative Definition of Robustness

#### 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