Improved estimation via model selection method for semimartingale regressions based on discrete data

TL;DR

This paper introduces a new model selection method for robust, adaptive nonparametric estimation of periodic functions in continuous-time regression models with semimartingale noise, improving estimation accuracy.

Contribution

It proposes a novel model selection approach tailored for semimartingale regression models, enhancing robustness and adaptivity in nonparametric estimation.

Findings

Demonstrates improved estimation accuracy over existing methods

Provides theoretical guarantees for the proposed estimator

Validates effectiveness through simulation studies

Abstract

We consider the robust adaptive nonparametric estimation problem for a periodic function observed in the framework of a continuous time regression model with semimartingale noises.