  This thesis deals with the nonparametric estimation of density f of the
regression error term E of the model Y=m(X)+E, assuming its independence with
the covariate X. The difficulty linked to this study is the fact that the
regression error E is not observed. In a such setup, it would be unwise, for
estimating f, to use a conditional approach based upon the probability
distribution function of Y given X. Indeed, this approach is affected by the
curse of dimensionality, so that the resulting estimator of the residual term E
would have considerably a slow rate of convergence if the dimension of X is
very high. Two approaches are proposed in this thesis to avoid the curse of
dimensionality. The first approach uses the estimated residuals, while the
second integrates a nonparametric conditional density estimator of Y given X.
If proceeding so can circumvent the curse of dimensionality, a challenging
issue is to evaluate the impact of the estimated residuals on the final
estimator of the density f. We will also attempt to determine the pointwise
rate of convergence of our proposed estimators. One our main aims is to
characterize the optimal choices of the first and second step bandwidths used
for estimating m and f respectively.
