Nonparametric deconvolution problem for dependent sequences
Abstract
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 meansquare 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 nonnoisy 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.4004
 Bibcode:
 2007arXiv0711.4004K
 Keywords:

 Mathematics  Statistics;
 62G05 (Primary) 62G07;
 60F05 (Secondary)
 EPrint:
 Published in at http://dx.doi.org/10.1214/07EJS154 the Electronic Journal of Statistics (http://www.ijournals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)