Open Access
2008 Nonparametric deconvolution problem for dependent sequences
Rafał Kulik
Electron. J. Statist. 2: 722-740 (2008). DOI: 10.1214/07-EJS154


We consider the nonparametric estimation of the density function of weakly and strongly dependent processes with noisy observations. We show that in the ordinary smooth case the optimal bandwidth choice can be influenced by long range dependence, as opposite to the standard case, when no noise is present. In particular, if the dependence is moderate the bandwidth, the rates of mean-square convergence and, additionally, central limit theorem are the same as in the i.i.d. case. If the dependence is strong enough, then the bandwidth choice is influenced by the strength of dependence, which is different when compared to the non-noisy case. Also, central limit theorem are influenced by the strength of dependence. On the other hand, if the density is supersmooth, then long range dependence has no effect at all on the optimal bandwidth choice.


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Rafał Kulik. "Nonparametric deconvolution problem for dependent sequences." Electron. J. Statist. 2 722 - 740, 2008.


Published: 2008
First available in Project Euclid: 13 August 2008

zbMATH: 1320.62073
MathSciNet: MR2430252
Digital Object Identifier: 10.1214/07-EJS154

Primary: 62G05
Secondary: 60F05 , 62G07

Keywords: Deconvolution , error-in-variables models , linear processes , Long range dependence

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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