Nonparametric estimation of a two dimensional continuous-discrete density function by wavelets

Christophe Chesneau*, Isha Dewan, Hassan Doosti

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the estimation of a two dimensional continuous-discrete density function. A new methodology based on wavelets is proposed. We construct a linear wavelet estimator and a non-linear wavelet estimator based on a term-by-term thresholding. Their rates of convergence are established under the mean integrated squared error over Besov balls. In particular, we prove that our adaptive wavelet estimator attains a fast rate of convergence. A simulation study illustrates the usefulness of the proposed estimators.

Original languageEnglish
Pages (from-to)64-78
Number of pages15
JournalStatistical Methodology
Volume18
DOIs
Publication statusPublished - May 2014
Externally publishedYes

Keywords

  • adaptivity
  • continuous-discrete density
  • density estimation
  • hard thresholding
  • wavelets

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