Non asymptotic sharp oracle inequalities for the improved model selection procedures for the adaptive nonparametric signal estimation problem

In this paper, we consider the robust adaptive non parametric estimation problem for the periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Sharp oracle inequalities for the robust risks have been obtained

Improved robust model selection methods for a Lévy nonparametric regression in continuous time

In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given

Improved estimation of a function in continuous regression with semimartingale noise

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Renewal theory and its applications : lectures notes for the course "Stochastic modelling" taken by most Mathematics students and Economics students (directions of training 01.03.01 - Mathematics and 38.04.01 - Economics)

The goal of the course is to study the main tools of the renewal theory and their applications to some problems of the actuarial analysis for insurance companies in the framework of the Cremer - Lundberg models. We consider such important problems in the renewal theory as limit theorems for the renewal process and the ruin problems for the insurance companies with investments in the stochastic financial markets. The notes areintended for students of the Mathematics and Economics Faculties

Model selection method for efficient signals processing from discrete data

The paper considers the problem of robust adaptiv