Moderate deviation principle for maximum-likelihood estimator

Abstract

In the present paper, we establish the moderate deviations principle for the maximum-likelihood estimator (MLE) from independent not identically sample under some suitable assumptions, which are weaker than the exponential integrability condition in Miao and Chen [Note on the moderate deviation principle of maximum likelihood estimator. Acta Appl Math. 2010;110:863–869] and give an equivalent condition of the moderate deviations principle for the MLE under the i.i.d. case.