Wavelet Based Estimation of the Derivatives of a Density for a Negatively Associated Process
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 Classification62G05 62G07
KeywordsNegative dependence Multiresolution analysis Besov space Wavelets Nonparametric estimation
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