Wavelet Based Estimation of the Derivatives of a Density for a Discrete-Time Stochastic Process: Lp-Losses

Abstract

We propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for such estimators. We suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quadratic characteristic.