On a Strictly Decreasing Nonparametric Estimator of the Drift Function for Recurrent Diffusion Processes

TL;DR

This paper introduces a new strictly decreasing nonparametric estimator for the drift function of recurrent diffusion processes, providing non-asymptotic risk bounds and a bandwidth selection method tailored to this framework.

Contribution

It presents a novel strictly decreasing estimator with risk bounds and bandwidth selection, specifically designed for recurrent diffusion processes.

Findings

Established non-asymptotic $ ext{L}^1$-risk bounds for the estimator

Developed a bandwidth selection procedure for the estimator

Applied the estimator to recurrent diffusion process drift estimation

Abstract

This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with non-asymptotic $\mathbb L^1$-risk bounds and a bandwidths selection procedure for a universal monotone estimator. These results are tailor-made to our framework, and then applied to the estimation of the drift function of recurrent diffusion processes in the second part of the paper.