Statistical Inference for Stochastic Processes

, Volume 11, Issue 3, pp 281–310 | Cite as

Root-n consistency in weighted L 1-spaces for density estimators of invertible linear processes

Article
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Abstract

The stationary density of an invertible linear processes can be estimated at the parametric rate by a convolution of residual-based kernel estimators. We have shown elsewhere that the convergence is uniform and that a functional central limit theorem holds in the space of continuous functions vanishing at infinity. Here we show that analogous results hold in weighted L 1-spaces. We do not require smoothness of the innovation density.

Keywords

Kernel estimator Plug-in estimator Tightness criteria Functional limit theorem Infinite-order moving average process Infinite-order autoregressive process 

AMS Subject Classification (2000)

Primary: 62G07 62G20 62M05 62M10 
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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesBinghamton UniversityBinghamtonUSA
  2. 2.Mathematisches InstitutUniversität zu KölnKölnGermany

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