What question did this study set out to answer?

This research aims to analyze the convergence properties of the maximum likelihood estimator in a Rayleigh diffusion model.

June 26, 2026

An exponential convergence rate of the maximum likelihood estimator in a Rayleigh diffusion process

Key Points

This research aims to analyze the convergence properties of the maximum likelihood estimator in a Rayleigh diffusion model.
Used parameter-dependent measure transformations for estimation.
Applied asymptotic analysis to derive convergence rates.
Established optimal uniform Berry-Esseen bounds and Cramér-type results.
Demonstrated a nonuniform exponential convergence rate for the maximum likelihood estimator.
Deriving an optimal Berry-Esseen bound enhances estimating accuracy.
Cramér-type results suggest effective moderate deviation assessments.

Abstract

This paper investigates the maximum likelihood estimator (MLE) for the drift coefficient in a Rayleigh diffusion model. Using parameter-dependent measure transformations and asymptotic analysis, we establish a nonuniform exponential convergence rate for the estimator. As a consequence, we derive an optimal uniform Berry-Esseen bound and Cramér-type moderate deviation results.

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