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April 2007 Uniformly root-n consistent density estimators for weakly dependent invertible linear processes
Anton Schick, Wolfgang Wefelmeyer
Ann. Statist. 35(2): 815-843 (April 2007). DOI: 10.1214/009053606000001352


Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n−1/2. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimators; these results are of independent interest.


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Anton Schick. Wolfgang Wefelmeyer. "Uniformly root-n consistent density estimators for weakly dependent invertible linear processes." Ann. Statist. 35 (2) 815 - 843, April 2007.


Published: April 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1117.62036
MathSciNet: MR2336870
Digital Object Identifier: 10.1214/009053606000001352

Primary: 62G07 , 62G20 , 62M05 , 62M10

Keywords: Functional limit theorem , infinite-order autoregressive process , infinite-order moving average process , Kernel estimator , least squares estimator , Plug-in estimator

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.35 • No. 2 • April 2007
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