Wavelet Estimation of Regression Derivatives for Biased and Negatively Associated Data

Abstract

This paper considers the estimation of the derivatives of a regression function based on biased data. The main feature of the study is to explore the case where the data comes from a negatively associated process. In this context, two different wavelet estimators are introduced: a linear wavelet estimator and a nonlinear wavelet estimator using the hard thresholding rule. Their theoretical performance is evaluated by determining sharp rates of convergence under L^p risk, assuming that the unknown function of interest belongs to a ball of Besov spaces B^s_p,q (ℝ). The obtained results extend some existing works on biased data in the independent case to the negatively associated case.