Analysis of least squares regression estimates in case of additional errors in the variables

Estimation of a regression function from independent and identical distributed data is considered. The L2 error with integration with respect to the design measure is used as error criterion. Upper bounds on the L2 error of least squares regression estimates are presented, which bound the error of the estimate in case that in the sample given to the estimate the values of the independent and the dependent variables are pertubated by some arbitrary procedure. The bounds are applied to analyze regression-based Monte Carlo methods for pricing American options in case of errors in modelling the price process.