Nonlinear wavelet estimator of the regression function under dependent biased data

In this paper, we define a new nonlinear wavelet-based estimator of the regression function based on a random sample from dependent biased data . We provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. We show that these estimators achieve nearly optimal minimax convergence rates within logarithmic terms over a large range of Besov function classes $B^s_{pq}$. It is also assumed that the observations form a stationary $\alpha$-mixing sequence.