Wavelet estimation in nonparametric model under martingale difference errors

Abstract

This paper is concerned with the heteroscedastic regression model Yi=g(xi)+σiei(1⩽i⩽n) under correlated errors ei, where it is assumed that σiEmphasis>/2=f(ui), the design points (xi, ui) are known and nonrandom, and g and f are unknown functions. Assuming that unobserved disturbances ei are martingale differences. The strong uniform convergence rates and r-th moment uniform convergence rates of wavelet estimator of g are investigated. Also, the strong uniform convergence rates are discussed for wavelet estimator of f.