  In this paper we develop the James - Stein improved estimation method for a
nonparametric periodic function observed with the Levy noises in continuous
time. An adaptive model selection procedure based on the improved weighted
least square estimates is constructed. The improvement effect for the
nonparametric models is obtained. It turns out that in the nonasymptotic
studies the accuracy improvement for nonparametric problems is more
significantly than for the parametric one. Moreover, sharp oracle inequalities
for the robust risks have been shown and the efficiency property for the
improved model selection procedure has been established in the adaptive
setting.
