Wavelet-based estimators of the integrated squared density derivatives for mixing sequences.

N.  Hosseinioun; H.  Doosti; H. A.  Niroumand

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Wavelet-based estimators of the integrated squared density derivatives for mixing sequences.

Author(s)

N. Hosseinioun Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Iran

H. Doosti Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Iran

H. A. Niroumand Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Iran

Abstract

The problem of estimation of the squared derivative of a probability density ƒ is considered using wavelet orthogonal bases. We obtain the precise asymptotic expression for the mean integrated error of the wavelet estimators when the process is strongly mixing. We show that the proposed estimator attains the same rate as when the observations are independent. Certain week dependence conditions are imposed to the {Xi} defined in {Ω, N, P).

Publication Details

Page(s) 341-350

DOI DOI not available

Published Journal: Pakistan Journal of Statistics, Volume: 25, Issue: 3, Year: 2009

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