A new parametric theory proves large deviation principles for Bayesian and maximum likelihood estimators in the moderate deviation zone along with uniform approximations and posterior concentration results.
Bahadur asymptotic efficiency in the zone of moderate deviation probabilities
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abstract
For a sequence of independent identically distributed random variables having a distribution function with an unknown parameter from a set $\Theta \subset \mathbf{R}^d$, we prove an analogue of the lower bound of Bahadur asymptotic efficiency for the zone of moderate deviation probabilities. The assumptions coincide with assumptions conditions under which the locally asymptotically minimax lower bound of Hajek-Le Cam was proved. The lower bound for local Bahadur asymptotic efficiency is a special case of this lower bound.
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Parametric Statistical Inference in the Zone of Moderate Deviation Probabilities
A new parametric theory proves large deviation principles for Bayesian and maximum likelihood estimators in the moderate deviation zone along with uniform approximations and posterior concentration results.