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March, 1994 Weak Convergence of Randomly Weighted Dependent Residual Empiricals with Applications to Autoregression
Hira L. Koul, Mina Ossiander
Ann. Statist. 22(1): 540-562 (March, 1994). DOI: 10.1214/aos/1176325383

Abstract

This paper establishes the uniform closeness of a randomly weighted residual empirical process to its natural estimator via weak convergence techniques. The weights need not be independent, bounded or even square integrable. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in $p$th-order autoregression models. The latter result, in turn, yields the asymptotic distributions of a class of robust and Jaeckel-type rank estimators. The main result is also used to obtain the asymptotic distributions of the least absolute deviation and certain other robust minimum distance estimators of the autoregression parameter vector.

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Hira L. Koul. Mina Ossiander. "Weak Convergence of Randomly Weighted Dependent Residual Empiricals with Applications to Autoregression." Ann. Statist. 22 (1) 540 - 562, March, 1994. https://doi.org/10.1214/aos/1176325383

Information

Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0836.62063
MathSciNet: MR1272098
Digital Object Identifier: 10.1214/aos/1176325383

Subjects:
Primary: 60F17
Secondary: 62M10

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 1 • March, 1994
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