Wavelet-Kernel Estimation of Regression Function for Uniformly Mixing Process

Methods of estimation of density and regression function are quite common in statistical applications. Wavelet theory has the potential to provide statisticians with powerful new techniques for nonparametric inference. It combines recent advances in approximation theory with insights gained from applied signal analysis. Nonparametric curve estimation by wavelets has been treated in numerous articles in various setups see, Antoniadis [1], Donoho [2] and Hardle [3]. The problem of interest is the estimation of nonparametric regression function based on the observations (X1, Y1), (X2, Y2),..., (Xn, Yn ). There are many interesting examples where applications of regression smoothing methods have yielded analysis essentially unobtainable by other techniques. Eubank [4] and Muller [5]. In contrast with most existing works Antoniadis [6], Delyon [7], Kovac and Silverman [8], Vidakovic [9] and Sardy [10], Antoniadis and Fan [11]. In this paper we consider wavelet estimator of regression function for uniformly mixing processes when the random design model is given as the