Adaptive wavelet estimation of a function from an m-dependent process with possibly unbounded m

Christophe Chesneau*, Hassan Doosti, Lewi Stone

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The estimation of a multivariate function from a stationary m-dependent process is investigated, with a special focus on the case where m is large or unbounded. We develop an adaptive estimator based on wavelet methods. Under flexible assumptions on the nonparametric model, we prove the good performances of our estimator by determining sharp rates of convergence under two kinds of errors: the pointwise mean squared error and the mean integrated squared error. We illustrate our theoretical result by considering the multivariate density estimation problem, the derivatives density estimation problem, the density estimation problem in a GARCH-type model and the multivariate regression function estimation problem. The performance of proposed estimator has been shown by a numerical study for a simulated and real data sets.

Original languageEnglish
Pages (from-to)1123-1135
Number of pages13
JournalCommunications in Statistics - Theory and Methods
Volume48
Issue number5
Early online date2018
DOIs
Publication statusPublished - 2019

Keywords

  • Density estimation
  • m-dependence
  • Nonparametric regression
  • Rates of convergence
  • Wavelet methods.

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