  This paper deals with the nonparametric estimation in heteroscedastic
regression $ Y_i=f(X_i)+\xi_i, \: i=1,...,n $, with incomplete information,
i.e. each real random variable $ \xi_i $ has a density $ g_{i} $ which is
unknown to the statistician. The aim is to estimate the regression function $ f
$ at a given point. Using a local polynomial fitting from M-estimator denoted $
\hat f^h $ and applying Lepski's procedure for the bandwidth selection, we
construct an estimator $ \hat f^{\hat h} $ which is adaptive over the
collection of isotropic H\"{o}lder classes. In particular, we establish new
exponential inequalities to control deviations of local M-estimators allowing
to construct the minimax estimator. The advantage of this estimator is that it
does not depend on densities of random errors and we only assume that the
probability density functions are symmetric and monotonically on $ \bR_+ $. It
is important to mention that our estimator is robust compared to extreme values
of the noise.
