  In this work, we develop and study an empirical projection operator scheme
for solving nonparametric regression problems. This scheme is based on an
approximate projection of the regression function over a suitable reproducing
kernel Hilbert space (RKHS). The RKHS considered in this paper are generated by
the Mercer kernels given by the Legendre Christoffel-Darboux and convolution
Sinc kernels. We provide error and convergence analysis of the proposed scheme
under the assumption that the regression function belongs to some suitable
functional spaces. We also consider the popular RKHS regularized least square
minimization for nonparametric regression. In particular, we check the
numerical stability of this second scheme and we provide its convergence rate
in the special case of the Sinc kernel. Finally, we illustrate the proposed
methods by various numerical simulation.
