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Journal of Statistical Theory and Practice

, Volume 2, Issue 3, pp 453–463 | Cite as

Wavelet Based Estimation of the Derivatives of a Density for a Negatively Associated Process

  • Yogendra P. Chaubey
  • Hassan Doosti
  • B. L. S. Prakasa Rao
Article

Abstract

Here we adopt the method of estimation for the derivatives of a probability density function based on wavelets discussed in Prakasa Rao (1996) to the case of negatively associated random variables. An upper bound on Lp-loss for the resulting estimator is given which extends such a result for the integrated mean square error (IMSE) given in Prakasa Rao (1996). Also, considering the case of derivative of order zero, the results given by Kerkyacharian and Picard (1992), Tribouley (1995) and Leblanc (1996) are obtained as special cases.

AMS Subject Classification

62G05 62G07 

Keywords

Negative dependence Multiresolution analysis Besov space Wavelets Nonparametric estimation 

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Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  • Yogendra P. Chaubey
    • 1
  • Hassan Doosti
    • 2
  • B. L. S. Prakasa Rao
    • 3
  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontréalCanada
  2. 2.Statistical Research and Training Center (SRTC), TehranIran & Department of Statistics, Ferdowsi UniversityMashhadIran
  3. 3.Department of Mathematics and StatisticsUniversity of HyderabadHyderabadIndia

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