Nonparametric regression with additional measurement errors in the dependent variable

Estimation of a regression function from data which consists of an independent and identically distributed sample of the underlying distribution with additional measurement errors in the dependent variable is considered. It is allowed that the measurement errors are not independent and have nonzero mean. It is shown that the rate of convergence of least-squares estimates applied to this data is similar to the rate of convergence of least-squares estimates applied to an independent and identically distributed sample of the underlying distribution as long as the measurement errors are small. As an application, estimation of conditional variance functions from residuals is considered.