Analysis of the rate of convergence of least squares neural network regression estimates in case of measurement errors.

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 independent variables is considered. It is allowed that the measurement errors are not independent and have a nonzero mean. It is shown that the rate of convergence of suitably defined least squares neural network estimates applied to this data is similar to the rate of convergence of least squares neural network estimates applied to an independent and identically distributed sample of the underlying distribution as long as the measurement errors are small.