Bahadur asymptotic efficiency in the zone of moderate deviation probabilities

M. S. Ermakov<sup>ab

a</sup> Saint Petersburg State University
^b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg

Abstract: We establish an analog of Bahadur's lower bound for asymptotic efficien-cy in the moderate deviation probabilities zone. We consider problems of parameter estimation for independent, not necessarily identically distribu-ted, random variables and signal in Gaussian white noise. The assertions are obtained under the same conditions under which the Hajek–Le Cam locally asymptotically minimax lower bound has been established. The Bahadur lower bound for local asymptotic efficiency is a special case of this lower bound.

Key words and phrases: Bahadur efficiency, large deviations, moderate deviations.

UDC: 519.2

Received: 22.10.2025