Nonparametric deconvolution problem for dependent sequences

Details Nonparametric deconvolution problem for dependent sequences Nonparametric deconvolution problem for dependent sequences

2007-11-26

arxiv.org/abs/0711.4004v2

Electronic Journal of Statistics 2008, Vol. 2, 722-740

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS154 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

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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