Plug-in estimators for higher-order transition densities in autoregression

Anton Schick; Wolfgang Wefelmeyer

ESAIM: Probability and Statistics (2009)

  • Volume: 13, page 135-151
  • ISSN: 1292-8100

Abstract

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In this paper we obtain root-n consistency and functional central limit theorems in weighted L1-spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based kernel estimator. These weights are chosen to exploit the fact 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.

How to cite

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Schick, Anton, and Wefelmeyer, Wolfgang. "Plug-in estimators for higher-order transition densities in autoregression." ESAIM: Probability and Statistics 13 (2009): 135-151. <http://eudml.org/doc/250669>.

@article{Schick2009,
abstract = { In this paper we obtain root-n consistency and functional central limit theorems in weighted L1-spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based kernel estimator. These weights are chosen to exploit the fact 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. },
author = {Schick, Anton, Wefelmeyer, Wolfgang},
journal = {ESAIM: Probability and Statistics},
keywords = {Empirical likelihood; Owen estimator; least dispersed regular estimator; efficient influence function; stochastic expansion of residual-based kernel density estimator; empirical likelihood; least dispersed regular estimator; stochastic expansion of residual-based kernel density estimator},
language = {eng},
month = {3},
pages = {135-151},
publisher = {EDP Sciences},
title = {Plug-in estimators for higher-order transition densities in autoregression},
url = {http://eudml.org/doc/250669},
volume = {13},
year = {2009},
}

TY - JOUR
AU - Schick, Anton
AU - Wefelmeyer, Wolfgang
TI - Plug-in estimators for higher-order transition densities in autoregression
JO - ESAIM: Probability and Statistics
DA - 2009/3//
PB - EDP Sciences
VL - 13
SP - 135
EP - 151
AB - In this paper we obtain root-n consistency and functional central limit theorems in weighted L1-spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based kernel estimator. These weights are chosen to exploit the fact 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.
LA - eng
KW - Empirical likelihood; Owen estimator; least dispersed regular estimator; efficient influence function; stochastic expansion of residual-based kernel density estimator; empirical likelihood; least dispersed regular estimator; stochastic expansion of residual-based kernel density estimator
UR - http://eudml.org/doc/250669
ER -

References

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