## Annals of Statistics

### The Behavior of Robust Estimators on Dependent Data

#### Abstract

This paper investigates the effect of serial dependence in the data on the efficiency of some robust estimators. When the observations are from a stationary process satisfying certain mixing conditions, linear combinations of order statistics and the Hodges-Lehmann estimator are shown to be asymptotically normally distributed. Gaussian processes are studied in detail and it is shown that when all the serial correlations $(\rho_n)$ are $\geqq 0$, the efficiency of the robust estimators relative to the mean is greater than in the case of independent observations.

#### Article information

Source
Ann. Statist., Volume 3, Number 5 (1975), 1070-1100.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343241

Digital Object Identifier
doi:10.1214/aos/1176343241

Mathematical Reviews number (MathSciNet)
MR395039

Zentralblatt MATH identifier
0359.62042

JSTOR