Resumen
We consider the estimation of non-parametric regression function with long memory data and investigate the asymptotic rates of convergence of wavelet estimators based on block thresholding. We show that the estimators achieve optimal minimax convergence rates over a large class of functions that involve many irregularities of a wide variety of types, including chirp and Doppler functions, and jump discontinuities. Therefore, in the presence of long memory noise, wavelet estimators still provide extensive adaptivity to many irregularities of large function classes.

Resumen
Wavelet-based density estimators with randomly right-censored data are considered. We investigate the asymptotic rates of convergence of estimators based on thresholding of empirical wavelet coefficients. Unlike the complete data case, the empirical wavelet coefficients are constructed through the Kaplan-Meier estimators of the distribution functions. It turns out that these coefficients can be approximated by an average of i.i.d. random variables with a certain error rate. We show that the estimators achieve nearly optimal minimax convergence rates within logarithmic terms over a large range of Besov function classes B"p"q^@a,@a>1/p,p>=1,q>=1, a feature not available for linear estimators when p<2.