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July, 1977 Behavior of Robust Estimators in the Regression Model with Dependent Errors
Hira L. Koul
Ann. Statist. 5(4): 681-699 (July, 1977). DOI: 10.1214/aos/1176343892


This paper proves the asymptotic linearity in the regression parameter of a class of linear rank statistics when errors in the regression model are strictly stationary and strongly mixing. Besides this, several other weak convergence results are proved which yield the asymptotic normality of $L$ and $M$ estimators of the regression parameter under the above dependent structure. All these results are useful in studying the effect of the above dependence on the asymptotic behavior of $R, M$ and $L$ estimators vis-a-vis the least squares estimator. An example of linear model with Gaussian errors is given where it is shown that the asymptotic efficiency of certain classes of $R, M$ and $L$ estimators relative to the least squared estimator is greater than or equal to its value under the usual independent errors model.


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Hira L. Koul. "Behavior of Robust Estimators in the Regression Model with Dependent Errors." Ann. Statist. 5 (4) 681 - 699, July, 1977.


Published: July, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0358.62032
MathSciNet: MR443213
Digital Object Identifier: 10.1214/aos/1176343892

Primary: 62G05
Secondary: 62G35

Keywords: $R, M, L$ estimators , Regression parameter , robustness , strongly mixing

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 4 • July, 1977
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