## The Annals of Statistics

### Robust Regression: Asymptotics, Conjectures and Monte Carlo

Peter J. Huber

#### Abstract

Maximum likelihood type robust estimates of regression are defined and their asymptotic properties are investigated both theoretically and empirically. Perhaps the most important new feature is that the number $p$ of parameters is allowed to increase with the number $n$ of observations. The initial terms of a formal power series expansion (essentially in powers of $p/n$) show an excellent agreement with Monte Carlo results, in most cases down to 4 observations per parameter.

#### Article information

Source
Ann. Statist. Volume 1, Number 5 (1973), 799-821.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176342503

Digital Object Identifier
doi:10.1214/aos/1176342503

Mathematical Reviews number (MathSciNet)
MR356373

Zentralblatt MATH identifier
0289.62033

JSTOR
links.jstor.org

#### Citation

Huber, Peter J. Robust Regression: Asymptotics, Conjectures and Monte Carlo. Ann. Statist. 1 (1973), no. 5, 799--821. doi:10.1214/aos/1176342503. http://projecteuclid.org/euclid.aos/1176342503.