IJPAM: Volume 27, No. 1 (2006)

WAVELET BASED ESTIMATION OF THE DERIVATIVES
OF A DENSITY WITH ASSOCIATED VARIABLES

Yogendra P. Chaubey$^1$, Hassan Doosti$^2$, B.L.S. Prakasa Rao$^3$
$^1$Department of Mathematics and Statistics
Concordia University
1455, de Maisonnekve Blvd. W.
Montreal, Quebec, H3G 1M8, CANADA
e-mail: chaubey@alcor.concordia.ca
$^2$Department of Statistics
Ferdowsi University
Mashhad, 91755-1159, IRAN
e-mail: doosti@math.um.ac.ir
$^3$Department of Mathematics and Statistics
University of Hyderabad
Hyderabad, 500 046, INDIA
e-mail: blsprsm@uohyd.ernet.in


Abstract.We propose a method of estimation of the derivatives of probability density based wavelets methods for a sequence of associated random variables with a common one-dimensional probability density function and obtain an upper bound on $L_p$-losses for the such estimators.

Received: February 21, 2006

AMS Subject Classification: 62G05, 62G07

Key Words and Phrases: associated dependence, multiresolution analysis, Besov space, wavelets, nonparametric estimation of derivative of density

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 27
Issue: 1