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Plug-in estimators for higher-ordertransition densities in autoregression

Published online by Cambridge University Press:  26 March 2009

Anton Schick  and
Wolfgang Wefelmeyer
Anton Schick
Affiliation:
Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA.
Wolfgang Wefelmeyer
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany; wefelm@math.uni.koeln.de
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Abstract

In this paper we obtain root-n consistency and functional central limittheorems in weighted L 1-spaces for plug-in estimators of thetwo-step transition density in the classical stationary linear autoregressivemodel of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-basedkernel estimator for the unknown innovation densityimproves on plugging in an unweighted residual-based kernel estimator. These weights are chosen to exploit thefact that the innovations have mean zero.If an efficient estimator for the autoregression parameter is used,then the weighted plug-in estimator for the two-step transition density is efficient. Our approach generalizes to invertible linear processes.

Keywords

Empirical likelihoodOwen estimatorleast dispersed regular estimatorefficient influence functionstochastic expansion of residual-based kernel density estimator
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 13 , July 2009 , pp. 135 - 151
Copyright
© EDP Sciences, SMAI, 2009

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