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.
Publié le : 1975-09-14
Classification:
Order statistics,
robust estimation,
strong mixing,
stationary processes,
relative efficiency,
62G35,
62E20,
60J99
@article{1176343241,
author = {Gastwirth, Joseph L. and Rubin, Herman},
title = {The Behavior of Robust Estimators on Dependent Data},
journal = {Ann. Statist.},
volume = {3},
number = {1},
year = {1975},
pages = { 1070-1100},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343241}
}
Gastwirth, Joseph L.; Rubin, Herman. The Behavior of Robust Estimators on Dependent Data. Ann. Statist., Tome 3 (1975) no. 1, pp. 1070-1100. http://gdmltest.u-ga.fr/item/1176343241/