The sharp lower bound of asymptotic efficiency of estimators in the zone of moderate deviation probabilities

DOI10.1214/12-EJS742zbMath1295.62019arXiv1206.1465OpenAlexW2964230297MaRDI QIDQ1950895

Mikhail Sergeevich Ermakov

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.1465

zbMATH Keywords

asymptotic efficiencylarge deviationsconfidence estimation

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Parametric tolerance and confidence regions (62F25) Point estimation (62F10) Large deviations (60F10)

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Cites Work

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• Delta method in large deviations and moderate deviations for estimators
• On density estimation in the view of Kolmogorov's ideas in approximation theory
• Mathematical theory of statistics. Statistical experiments and asymptotic decision theory
• Moderate and Cramér-type large deviation theorems for M-estimators
• Estimators and spread
• On probabilities of large deviations in Banach spaces
• On large deviations for sums of random vectors in \(R_ k\).
• Strong moderate deviation theorems
• On large-deviation efficiency in statistical inference
• Spread, estimators and nuisance parameters
• Asymptotics and the theory of inference
• On semiparametric statistical inferences in the moderate deviation zone
• Multi-dimensional integral limit theorems for large deviations
• Likelihood Asymptotics
• Approximation Theorems of Mathematical Statistics
• Lower Bounds for Probabilities of Large Deviations for Sums of Independent Random Variables
• Probabilities of Large Deviations for U-Statistics and von Mises Functionals
• Importance sampling for simulations of moderate deviation probabilities of statistics
• Saddlepoint Approximations with Applications
• Asymptotic Statistics
• On Asymptotically Efficient Statistical Inference for Moderate Deviation Probabilities
• On Large and Superlarge Deviations of Sums of Independent Random Vectors Under Cramér's Condition. II
• Asymptotic Efficiency of the Maximum Likelihood Estimator