Non-parametric estimation in a semimartingale regression model. Part 1. Oracle Inequalities

TL;DR

This paper introduces a new adaptive model selection procedure for estimating periodic functions in continuous time regression models with semimartingale noise, providing sharp non-asymptotic oracle inequalities.

Contribution

It proposes a novel adaptive estimation method with sharp oracle inequalities for semimartingale regression models, advancing non-parametric estimation techniques.

Findings

Derived sharp non-asymptotic oracle inequalities.

Established the effectiveness of the adaptive procedure.

Enhanced estimation accuracy in semimartingale models.

Abstract

This paper considers the problem of estimating a periodic function in a continuous time regression model with a general square integrable semimartingale noise. A model selection adaptive procedure is proposed. Sharp non-asymptotic oracle inequalities have been derived.