Wavelet-Based estimation of multivariate regression functions in besov spaces*

Abstract

Let (Y, X) = {Y i , X i } be real-valued jointly stationary processes and let ρ be a Borel measurable function on the real line. Let be a d-dimensional regression function. For regression functions in the Besov space B s,p,q we estimate g using orthonormal wavelet bases. Uniform rates of almost sure convergence over compact subsets of R d are established for strongly mixing processes.