Annals of Statistics

The Behavior of Robust Estimators on Dependent Data

Joseph L. Gastwirth and Herman Rubin

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62G35: Robustness
Secondary: 62E20: Asymptotic distribution theory 60J99: None of the above, but in this section

Keywords
Order statistics robust estimation strong mixing stationary processes relative efficiency

Citation

Gastwirth, Joseph L.; Rubin, Herman. The Behavior of Robust Estimators on Dependent Data. Ann. Statist. 3 (1975), no. 5, 1070--1100. doi:10.1214/aos/1176343241. https://projecteuclid.org/euclid.aos/1176343241


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