The Sharp Lower Bound of Asymptotic Efficiency of Estimators in the Zone of Moderate Deviation Probabilities

TL;DR

This paper establishes a fundamental lower bound on the efficiency of estimators in the context of moderate deviation probabilities for multidimensional parameters, providing insights into confidence estimation limits.

Contribution

It introduces the first local asymptotic minimax lower bound for estimator efficiency in the moderate deviation zone for multidimensional parameters.

Findings

Lower bound interpreted as efficiency limit in confidence estimation

Applicable to multidimensional parameter estimation

Advances understanding of estimator performance in moderate deviations

Abstract

For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the lower bound of asymptotic efficiency in confidence estimation.