Wavelet estimation in nonparametric model under martingale difference errors

This paper is concerned with the heteroscedastic regression model Y i=g(x i)+σ iei(1⩽i⩽n) under correlated errors e i, where it is assumed that σ i Emphasis>/2 =f(u i), the design points (x i, ui) are known and nonrandom, and g and f are unknown functions. Assuming that unobserved disturbances e i 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.