2012
DOI: 10.1214/12-ejs742
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The sharp lower bound of asymptotic efficiency of estimators in the zone of moderate deviation probabilities

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.

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Cited by 24 publications
(27 citation statements)
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“…4. For estimation of accuracy of linear approximation of stochastic part of logarithm of likelihood ratio we prove the following inequalities (see Lemma4.2 and, for comparison, (3.4) and Lemma 5.3 in [14]). For any θ j , θ k ∈ Λ ǫ ∩ K ije and κ > 0, there holds…”
Section: Proof Of Theorem 25mentioning
confidence: 99%
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“…4. For estimation of accuracy of linear approximation of stochastic part of logarithm of likelihood ratio we prove the following inequalities (see Lemma4.2 and, for comparison, (3.4) and Lemma 5.3 in [14]). For any θ j , θ k ∈ Λ ǫ ∩ K ije and κ > 0, there holds…”
Section: Proof Of Theorem 25mentioning
confidence: 99%
“…5. The estimates of (4.2) and (4.3) -type and "chaining" method allow to implement to addendums of right-hand side of (4.1) the technique of the proof of multidimensional local asymptotic minimax lower bound [2] on the base of the same reasoning as in [14].…”
Section: Proof Of Theorem 25mentioning
confidence: 99%
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“…Like large deviations, the moderate deviation problems arise in the theory of statistical inference quite naturally. The moderate deviation principle (MDP for short) can provide us with the rate of convergence and a useful method for constructing asymptotic confidence intervals, see [13,17] and references therein.…”
Section: Introductionmentioning
confidence: 99%