A FORMULATION FOR MEAN INTEGRATED SQUARED ERROR OF NONLINEAR WAVELET-BASED DENSITY ESTIMATORS WITH NEGATIVELY DEPENDENT SEQUENCES

N. Hosseinioun (Iran), H. A. Nirumand (Iran) and H. Doosti (Iran)

Received January 20, 2008

Abstract

We provide an asymptotic expansion for mean integrated error (MISE) of nonlinear wavelet-based estimators with negatively dependent random variables. Our technique is analogous to that of Hall and Patil [7] and is facillated by the result of Amini and Bozorgnia [1] that presented bound for probabilities with negatively dependent random variables.

Keywords and phrases: bandwidth, MISE expansion, Fourier series, threshold, density estimation, mean integrated square error, multiresolution, wavelet, negatively dependent.