On goodness-of-fit tests for parametric hypotheses in perturbed dynamical systems using a minimum distance estimator

TL;DR

This paper develops an asymptotically distribution-free goodness-of-fit test for parametric hypotheses in diffusion processes observed continuously with small noise, utilizing a minimum distance estimator for the unknown parameter.

Contribution

It introduces a novel goodness-of-fit test that is asymptotically distribution-free for diffusion processes with small noise, based on a minimum distance estimator.

Findings

The test is asymptotically distribution-free.

It effectively detects deviations from the null hypothesis.

Applicable to continuous-time diffusion models with small noise.

Abstract

We consider the problem of the construction of the Goodness-of-Fit test in the case of continuous time observations of a diffusion process with small noise. The null hypothesis is parametric and we use a minimum distance estimator of the unknown parameter. We propose an asymptotically distribution free test for this model.