# 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

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topSchick, 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 -

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