Wavelet based estimation of the derivatives of a density for a negatively associated process

Yogendra P. Chaubey; Hassan Doosti; B. L. S. Prakasa Rao

doi:10.1080/15598608.2008.10411886

Wavelet based estimation of the derivatives of a density for a negatively associated process

Yogendra P. Chaubey, Hassan Doosti, B. L. S. Prakasa Rao

Research output: Contribution to journal › Article

14 Citations (Scopus)

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 L_p-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.

Original language	English
Pages (from-to)	453-463
Number of pages	11
Journal	Journal of Statistical Theory and Practice
Volume	2
Issue number	3
DOIs	https://doi.org/10.1080/15598608.2008.10411886
Publication status	Published - 2008
Externally published	Yes

Keywords

Besov space
multiresolution analysis
negative dependence
nonparametric estimation
wavelets

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10.1080/15598608.2008.10411886

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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.",

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AU - Chaubey, Yogendra P.

AU - Doosti, Hassan

AU - Prakasa Rao, B. L. S.

PY - 2008

Y1 - 2008

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AB - 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.

KW - Besov space

KW - multiresolution analysis

KW - negative dependence

KW - nonparametric estimation

KW - wavelets

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JO - Journal of Statistical Theory and Practice

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