Uniformly root-n consistent density estimators for weakly dependent invertible linear processes
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The Annals of Statistics

Uniformly root-n consistent density estimators for weakly dependent invertible linear processes

Anton Schick and Wolfgang Wefelmeyer

Source: Ann. Statist. Volume 35, Number 2 (2007), 815-843.

Abstract

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.

Primary Subjects: 62G07, 62G20, 62M05, 62M10
Keywords: Least squares estimator; kernel estimator; plug-in estimator; functional limit theorem; infinite-order moving average process; infinite-order autoregressive process

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Permanent link to this document: http://projecteuclid.org/euclid.aos/1183667295
Digital Object Identifier: doi:10.1214/009053606000001352
Mathematical Reviews number (MathSciNet): MR2336870

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