Large deviations for M-estimators

DOI10.1007/S10463-005-0017-5zbMath1097.62013OpenAlexW2018195534MaRDI QIDQ2502131

Miguel A. Arcones

Publication date: 12 September 2006

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10463-005-0017-5

zbMATH Keywords

M-estimatorsKullback-Leibler informationLarge deviationsMaximum likelihood estimatorsEmpirical processes

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Parametric tolerance and confidence regions (62F25) Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30) Large deviations (60F10)

Related Items (10)

Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution ⋮ Statistical inference for the intensity in a partially observed jump diffusion ⋮ Limit theorems for deviation means of independent and identically distributed random variables ⋮ On some connections between Esscher's tilting, saddlepoint approximations, and optimal transportation: a statistical perspective ⋮ Moderate deviations inequalities for Gaussian process regression ⋮ Large deviation principle for moderate deviation probabilities of bootstrap empirical measures ⋮ Chernoff index for Cox test of separate parametric families ⋮ Delta method in large deviations and moderate deviations for estimators ⋮ Moderate deviations of generalized method of moments and empirical likelihood estimators ⋮ An inverse Sanov theorem for exponential families

Cites Work

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• On large deviation expansion of distribution of maximum likelihood estimator and its application in large sample estimation
• An extension of Sanov's theorem: Application to the Gibbs conditioning principle
• Approximation Theorems of Mathematical Statistics
• Location and Scale Parameters in Exponential Families of Distributions
• Uniform Central Limit Theorems
• Asymptotic Efficiency of Nonparametric Tests
• The Large Deviation Principle for Stochastic Processes. Part I
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