Open Access
February 1996 Asymptotics of some estimators and sequential residual empiricals in nonlinear time series
Hira L. Koul
Ann. Statist. 24(1): 380-404 (February 1996). DOI: 10.1214/aos/1033066216


This paper establishes the asymptotic uniform linearity of M- and R-scores in a family of nonlinear time series and regression models. It also gives an asymptotic expansion of the standardized sequential residual empirical process in these models. These results are, in turn, used to obtain the asymptotic normality of certain classes of M-, R- and minimum distance estimators of the underlying parameters. The classes of estimators considered include analogs of Hodges-Lehmann, Huber and LAD (least absolute deviation) estimators. Some applications to the change point and testing of the goodness-of-fit problems in threshold and amplitude-dependent exponential autoregression models are also given. The paper thus offers a unified functional approach to some aspects of robust inference for a large class of nonlinear time series models.


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Hira L. Koul. "Asymptotics of some estimators and sequential residual empiricals in nonlinear time series." Ann. Statist. 24 (1) 380 - 404, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0865.62065
MathSciNet: MR1389897
Digital Object Identifier: 10.1214/aos/1033066216

Primary: 60F17
Secondary: 62M10

Keywords: Asymptotic uniform linearity , asymptotically distribution free , change point , Goodness-of-fit , minimum distance estimators , threshold autoregression models

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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