The Annals of Statistics
- Ann. Statist.
- Volume 39, Number 2 (2011), 1211-1240.
Delta method in large deviations and moderate deviations for estimators
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Abstract
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large deviations is proposed. The new method can be widely applied to driving the moderate deviations of estimators and is illustrated by examples including the Wilcoxon statistic, the Kaplan–Meier estimator, the empirical quantile processes and the empirical copula function. We also improve the existing moderate deviations results for M-estimators and L-statistics by the new method. Some applications of moderate deviations to statistical hypothesis testing are provided.
Article information
Source
Ann. Statist. Volume 39, Number 2 (2011), 1211-1240.
Dates
First available in Project Euclid: 9 May 2011
Permanent link to this document
http://projecteuclid.org/euclid.aos/1304947048
Digital Object Identifier
doi:10.1214/10-AOS865
Mathematical Reviews number (MathSciNet)
MR2816352
Zentralblatt MATH identifier
1216.62027
Subjects
Primary: 60F10: Large deviations 62G20: Asymptotic properties
Secondary: 62F12: Asymptotic properties of estimators
Keywords
Delta method hypothesis testing Kaplan–Meier estimator large deviations L-statistics M-estimator moderate deviations
Citation
Gao, Fuqing; Zhao, Xingqiu. Delta method in large deviations and moderate deviations for estimators. Ann. Statist. 39 (2011), no. 2, 1211--1240. doi:10.1214/10-AOS865. http://projecteuclid.org/euclid.aos/1304947048.
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