Asymptotic Theory of M-Estimators in General Statistical Models. Part 1: OnAsymptotic Behavior of Estimators under Model Disturbance

摘要

Asymptotics of parameter estimators in a general scheme of statistical modelsdefined on a given probability space with filtration are discussed. The asymptotic behavior of estimators are studied and defined as solutions to certain equations (M-estimators). The representation of likelihood ratios in the form of exponential martingales is shown to be useful for application of martingale limit theorems. The conventional notations of martingale theory are used. Several examples of particular schemes of models are given.