Asymptotic Theory for the Multiscale Wavelet Density Derivative Estimator
Toshimitsu Ochiai, Kanta Naito · Communication in Statistics- Theory and Methods · 2003
In this paper we consider the wavelet-based estimation of density derivatives. The multiscale density derivative estimator is proposed which is constructed by using a number of scaling functions. Asymptotic theory is developed in which asymptotic expressions for the bias, the variance and the mean integrated squared error are included. In addition, asymptotic normality of the proposed estimator is proved. Theoretical and numerical comparisons with the usual kernel-based estimators are also reported.