Wavelet linear estimation for derivatives of a density from observations of mixtures with varying mixing proportions

Abstract

A wavelet based linear estimator is proposed for the derivatives of a probability density function based on a sample from a finite mixture of components with varying mixing proportions. It extends the linear estimator of a probability density function proposed by Pokhyl'ko (Theor. Probability and Math. Statist, 70 (2005) 135–145). Upper bounds on L₂ and L_∞ losses are obtained for such estimators.