Wavelet based estimation for the derivative of a density by block thresholding under random censorship

Esmaeil Shirazi*, Yogendra P. Chaubey, Hassan Doosti, Hossein Ali Nirumand

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We consider wavelet based method for estimating derivatives of a density via block thresholding when the data obtained are randomly right censored. The proposed method is analogous to that of Hall and Patil (1995) for density estimation in the complete data case that has been extended recently by Li (2003, 2008). We find bounds for the L 2-loss over a large range of Besov function classes for the resulting estimators. The results of Hall and Patil (1995), Prakasa Rao (1996) and Li (2003, 2008) are obtained as special cases and the performance of the proposed estimator is investigated by a numerical study.

Original languageEnglish
Pages (from-to)199-211
Number of pages13
JournalJournal of the Korean Statistical Society
Volume41
Issue number2
DOIs
Publication statusPublished - Jun 2012
Externally publishedYes

Keywords

  • Adaptive estimation
  • Block thresholding
  • Censored data
  • Nonparametric estimator of derivative of a density
  • Primary
  • Rates of convergence
  • Secondary

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