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

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.