ESTIMATION OF THE INTEGRATED SQUARED DENSITY DERIVATIVES BY WAVELETS

Abstract

The problem of estimation of the integral of the squared derivative of a probability density $f$ is considered using wavelet orthonormal bases. For $f$ such that $f^{(d)}$, the $d$-th derivative belongs to the Sobolev space $H_2^s , s > 0$, we obtain the precise asymptotic expression for the mean integrated squared error of the wavelet estimator