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Wavelet density estimation for negatively associated stratified size-biased sample

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  • Youming Liu
  • Junlian Xu

Abstract

This paper provides upper bounds of wavelet estimations on L -super- p (1≤ p >∞) risk for a density function in Besov spaces based on negatively associated stratified size-biased random samples. It turns out that the classical theorem of Donoho, Johnstone, Kerkyacharian and Picard is completely extended to more general cases. More precisely, we consider the model with multiplication noise and allow the sample negatively associated. Our theory is illustrated with a simulation study.

Suggested Citation

  • Youming Liu & Junlian Xu, 2014. "Wavelet density estimation for negatively associated stratified size-biased sample," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 537-554, September.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:537-554
    DOI: 10.1080/10485252.2014.930142
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    References listed on IDEAS

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    1. Christophe Chesneau & Isha Dewan & Hassan Doosti, 2012. "Wavelet linear density estimation for associated stratified size-biased sample," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 429-445.
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    Cited by:

    1. Renyu Ye & Xinsheng Liu & Yuncai Yu, 2020. "Pointwise Optimality of Wavelet Density Estimation for Negatively Associated Biased Sample," Mathematics, MDPI, vol. 8(2), pages 1-12, February.

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