Nonparametric regression with correlated errors

Nonparametric regression techniques are often sensitive to the presence of correlation in the errors. The practical consequences of this sensitivity a re explained, including the breakdown of several popular data-driven smooth ing parameter selection methods. We review the existing literature in kerne l regression, smoothing splines and wavelet regression under correlation, b oth for short-range and long-range dependence. Extensions to random design, higher dimensional models and adaptive estimation are discussed.