Multiplicative censoring: estimation of a density and its derivatives under the Lp-risk

Mohammad Abbaszadeh, Christophe Chesneau, Hassan Doosti

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We consider the problem of estimating a density and its derivatives for a sample of multiplicatively censored random variables. The purpose of this paper is to present an approach to this problem based on wavelets methods. Two different estimators are developed: a linear based on projections and a nonlinear using a term-by-term selection of the estimated wavelet coefficients. We explore their performances under the Lp-risk with p ≥ 1 and over a wide class of functions: the Besov balls. Fast rates of convergence are obtained. Finite sample properties of the estimation procedure are studied on a simulated data example.

Original languageEnglish
Pages (from-to)255-276
Number of pages22
JournalRevstat Statistical Journal
Volume11
Issue number3
Publication statusPublished - Nov 2013
Externally publishedYes

Keywords

  • Besov balls
  • Density estimation
  • Inverse problem
  • L-risk
  • Multiplicative censoring
  • Wavelets

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