Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences

N. Hosseinioun*, H. Doosti, H. A. Nirumand

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

The problem of estimation of the derivative of a probability density f is considered, using wavelet orthogonal bases. We consider an important kind of dependent random variables, the so-called mixing random variables and investigate the precise asymptotic expression for the mean integrated error of the wavelet estimators. We show that the mean integrated error of the proposed estimator attains the same rate as when the observations are independent, under certain week dependence conditions imposed to the {X i}, defined in {Ω, N, P}.

Original languageEnglish
Pages (from-to)195-203
Number of pages9
JournalStatistical Papers
Volume53
Issue number1
DOIs
Publication statusPublished - Feb 2012
Externally publishedYes

Keywords

  • Mixing sequences
  • Nonparametric estimation of a density
  • Scaling function
  • Wavelet function

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