Adaptive estimation in a heteroscedastic nonparametric regression

The paper considers the problem of estimating the unknown function of heteroscedastic regression. An adaptive model selection procedure based on improved weighted estimates of least squares with specially selected weight coefficients is proposed. It is established that the procedure has a higher mean-square accuracy than the procedure based on classical weighted least-squares estimates. For the mean square risk of the proposed procedure, a non-asymptotic oracle inequality is proved that determines the exact upper bound for it in all possible estimates. The results of numerical simulation are given.