Multivariate wavelet-based density estimation with size-biased data

Esmaeil Shirazi*, Hassan Doosti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


In this paper, we employ wavelet method to propose a multivariate density estimator based on a biased sample. We investigate the asymptotic rate of convergence of the proposed estimator over a large class of densities in the Besov space, Bpqs. Moreover, we prove the consistency of our estimator when the expectation of weight function is unknown. This paper is an extension of results in Ramirez and Vidakovic (2010) and Chesneau etal. (2012) to the multivariate case.

Original languageEnglish
Pages (from-to)12-19
Number of pages8
JournalStatistical Methodology
Publication statusPublished - 1 Nov 2015
Externally publishedYes


  • Besov spaces
  • Density estimation
  • Size-biased data
  • Wavelet


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