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Sankhya A

, Volume 76, Issue 1, pp 48–76 | Cite as

On the estimation of density-weighted average derivative by wavelet methods under various dependence structures

  • Christophe Chesneau
  • Maher Kachour
  • Fabien Navarro
Article

Abstract

The problem of estimating the density-weighted average derivative of a regression function is considered. We present a new consistent estimator based on a plug-in approach and wavelet projections. Its performances are explored under various dependence structures on the observations: the independent case, the ρ-mixing case and the α-mixing case. More precisely, denoting n the number of observations, in the independent case, we prove that it attains 1/n under the mean squared error, in the ρ-mixing case, \(1/\sqrt{n}\) under the mean absolute error, and, in the α-mixing case, \(\sqrt{\ln n /n}\) under the mean absolute error. A short simulation study illustrates the theory.

Keywords and phrases.

Nonparametric estimation of density-weighted average derivative ‘plug-in’ approach, wavelets  consistency ρ-mixing α-mixing 

AMS (2000) subject classification.

Primary 62G08 Secondary 62G20 Secondary 

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Copyright information

© Indian Statistical Institute 2013

Authors and Affiliations

  • Christophe Chesneau
    • 1
  • Maher Kachour
    • 2
  • Fabien Navarro
    • 1
    • 3
  1. 1.Département de Mathématiques, UFR de Sciences, LMNOUniversité de Caen Basse-NormandieCaen CedexFrance
  2. 2.École supérieure de commerce IDRACLyon Cedex 09France
  3. 3.GREYC CNRS-ENSICAEN-Université de CaenCaen CedexFrance

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