Efficient estimation for nonparametric regression with small intensity noise

Jeudi 28 octobre 2021, 10:15 à 11:15

Salle de séminaires M.0.1

Evgeny A. Pchelintsev

Tomsk State University, Russie.

We develop an efficient nonparametric estimation theory for continuous time regression models with non-Gaussian Lévy noises in the case when the unknown functions belong to Sobolev ellipses. Using the Pinsker’s approach, we provide a sharp lower bound for the normalized asymptotic mean square accuracy. We find constructive sufficient conditions for the ellipse coefficients under which we develop efficient estimation methods. We show that the obtained conditions hold for the ellipse coefficients of an exponential form.