Moderate deviations for estimators under exponentially stochastic differentiability conditions

Abstract

We introduce two exponentially stochastic differentiability conditions to study moderate deviations for M-estimators. Under a generalized exponentially stochastic differentiability condition, a moderate deviation principle is established. Some sufficient conditions of the exponentially stochastic differentiability and examples are also given.

Key words： M-estimator; exponentially stochastic differentiability; moderate deviations

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