statistics

On a Universal Strictly Decreasing Nonparametric Estimator Applied to the Drift Function of a Recurrent Diffusion Process Estimation

arXiv:2603.14037

summary

The paper proposes a continuously differentiable, strictly decreasing nonparametric estimator for the drift function of recurrent diffusion processes, providing non‑asymptotic L¹ risk bounds and a data‑driven bandwidth selection method.

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 -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.

17 pages, 2 figures

Topics & keywords

#nonparametric estimation#monotone estimator#drift function#recurrent diffusion processes#bandwidth selectionL1 risk boundsuniversal monotone estimatorstochastic differential equationsdiffusion drift estimationbandwidth selection procedure
On a Universal Strictly Decreasing Nonparametric Estimator Applied to the Drift Function of a Recurrent Diffusion Process Estimation · wovepaper