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April 2011 Delta method in large deviations and moderate deviations for estimators
Fuqing Gao, Xingqiu Zhao
Ann. Statist. 39(2): 1211-1240 (April 2011). DOI: 10.1214/10-AOS865


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.


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Fuqing Gao. Xingqiu Zhao. "Delta method in large deviations and moderate deviations for estimators." Ann. Statist. 39 (2) 1211 - 1240, April 2011.


Published: April 2011
First available in Project Euclid: 9 May 2011

zbMATH: 1216.62027
MathSciNet: MR2816352
Digital Object Identifier: 10.1214/10-AOS865

Primary: 60F10 , 62G20
Secondary: 62F12

Keywords: Delta method , Hypothesis testing , Kaplan–Meier estimator , large deviations , L-statistics , M-estimator , Moderate deviations

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 2 • April 2011
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