LAMN in a class of parametric models for null recurrent diffusion

TL;DR

This paper investigates statistical inference for null recurrent diffusion models, establishing LAMN property, minimax bounds, and optimal estimators for parameters influencing the drift, with a focus on the principal and secondary parameters.

Contribution

It introduces a novel analysis of null recurrent diffusions, deriving LAMN and optimal estimation procedures for models with multiple drift parameters.

Findings

LAMN property established for the models

Asymptotic minimax bounds derived

Explicit asymptotically optimal estimators specified

Abstract

We study statistical models for one-dimensional diffusions which are recurrent null. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A finite number of other parameters, of secondary importance, introduces additional flexibility for the modelization of the drift, and does not perturb the null recurrent behaviour. Under time-continuous observation we obtain local asymptotic mixed normality (LAMN), state a local asymptotic minimax bound, and specify asymptotically optimal estimators.