TY - JOUR
T1 - Wavelet based estimation of the derivatives of a density for a negatively associated process
AU - Chaubey, Yogendra P.
AU - Doosti, Hassan
AU - Prakasa Rao, B. L. S.
PY - 2008
Y1 - 2008
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=85008776553&partnerID=8YFLogxK
U2 - 10.1080/15598608.2008.10411886
DO - 10.1080/15598608.2008.10411886
M3 - Article
AN - SCOPUS:85008776553
SN - 1559-8608
VL - 2
SP - 453
EP - 463
JO - Journal of Statistical Theory and Practice
JF - Journal of Statistical Theory and Practice
IS - 3
ER -