LAMN in a class of parametric models for null recurrent diffusion
Statistics Theory
2017-11-07 v1 Statistics Theory
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.
Cite
@article{arxiv.1711.01776,
title = {LAMN in a class of parametric models for null recurrent diffusion},
author = {Reinhard Höpfner and Carina Zeller},
journal= {arXiv preprint arXiv:1711.01776},
year = {2017}
}