Open Access
September, 1975 The Behavior of Robust Estimators on Dependent Data
Joseph L. Gastwirth, Herman Rubin
Ann. Statist. 3(5): 1070-1100 (September, 1975). DOI: 10.1214/aos/1176343241


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.


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Joseph L. Gastwirth. Herman Rubin. "The Behavior of Robust Estimators on Dependent Data." Ann. Statist. 3 (5) 1070 - 1100, September, 1975.


Published: September, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0359.62042
MathSciNet: MR395039
Digital Object Identifier: 10.1214/aos/1176343241

Primary: 62G35
Secondary: 60J99 , 62E20

Keywords: order statistics , relative efficiency , robust estimation , Stationary processes , Strong mixing

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 5 • September, 1975
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