Improved model selection method for an adaptive estimation in semimartingale regression models

The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent dis- turbances given by a general square

Keywords: Non-parametric regression; Model selection; Sharp oracle inequal- ity; Robust risk; Asymptotic efficiency; Pinsker constant; Semimartingale noise.. AMS 2000

Fourdrinier and Pergamenshchikov [5] extended the Barron-Birge-Massart method to the models with dependent observations and, in contrast to all above-mentioned papers on the

In Section 3 it is shown that the problem of estimating parameter θ in (1) can be reduced to that of estimating the mean in a conditionally Gaussian distribution with a

The first goal of the research is to construct an adap- tive procedure based on observations (y j ) 1≤j≤n for estimating the function S and to obtain a sharp non-asymptotic upper

As to the nonparametric estimation problem for heteroscedastic regression models we should mention the papers Efromovich, 2007, Efromovich, Pinsker, 1996, and

In this case we chose the weight coefficients on the basis of the model selection procedure proposed in [14] for the general semi-martingale regression model in continuous time..

Asymptotic efficiency, model selection, non- parametric regression, Ornstein-Uhlenbeck pro- cess, periodic signals, robust quadratic risk, sharp oracle inequality, shrinkage