Wavelet Estimation of Regression Derivatives for Biased and Negatively Associated Data
Keywords:Regression derivatives estimation, negatively associated, Lp risk, wavelets
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 Lp risk, assuming that the unknown function of interest belongs to a ball of Besov spaces Bsp,q (ℝ). The obtained results extend some existing works on biased data in the independent case to the negatively associated case.
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