Super-efficient robust estimation in Lévy continuous time regression models from discrete data

In this paper we consider the nonparametric estimation problem for a continuous time regression model with non-Gaussian Lévy noise of small intensity. The estimation problem is studied under the condition that the observations are accessible only at discrete time moments. In this paper, based on the nonparametric estimation method, a new estimation procedure is constructed, for which it is shown that the rate of convergence, up to a certain logarithmic coefficient, is equal to the parametric one, i.e., super-efficient property is provided. Moreover, in this case, the Pinsker constant for the Sobolev ellipse with the geometrically increasing coefficients is calculated, which turns out to be the same as for the case of complete observations.