Nonlinear wavelet estimation of regression function with random desigm

The nonlinear wavelet estimator of regression function with random design i s constructed. The optimal uniform convergence rate of the estimator in a b all of Besov space B-p,q(s), is proved under quite general assumpations. Th e adaptive nonlinear wavelet estimator with near-optimal convergence rate i n a wide range of smoothness function classes is also constructed. The prop erties of the nonlinear wavelet estimator given for random design regressio n and only with bounded third order moment of the error can be compared wit h those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error.