In this paper we consider the nonparametric estimation problem for the diffusion signal on the basis of discrete data with unknown diffusion coefficients. For this problem through the truncated sequential point wise kernel estimators we construct a new improved model selection procedure for which we show oracle inequalities for arbitrary orthonormal basis on the grid, i.e. we show, that the constructed model selection procedure is optimal in the sharp oracle inequalities sense.
Перспективы развития фундаментальных наук : сборник научных трудов XVIII Международной конференции студентов, аспирантов и молодых ученых, 27–30 апреля 2021 г.. Томск, 2021. Т. 3 : Математика. С. 70-72