Quantile coupling inequalities and their applications

DOI10.1214/12-PS198zbMath1307.62036MaRDI QIDQ1950174

David M. Mason, Harrison H. Zhou

Publication date: 10 May 2013

Published in: Probability Surveys (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ps/1354125785

zbMATH Keywords

large deviationasymptotic equivalencefunction estimationquantile couplingKMT construction

Mathematics Subject Classification ID

Theory of statistical experiments (62B15) Nonparametric estimation (62G05) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (14)

The method of cumulants for the normal approximation ⋮ KMT coupling for random walk bridges ⋮ An improvement of Tusnády's inequality in the bulk ⋮ Cramér moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications ⋮ Gaussianization machines for non-Gaussian function estimation models ⋮ A quantile inequality for location-scale distributions ⋮ From \(p\)-Wasserstein bounds to moderate deviations ⋮ Central limit theorem and near classical Berry-Esseen rate for self normalized sums in high dimensions ⋮ Characterization of \(H\)-Brownian Gibbsian line ensembles ⋮ Strong approximations for the \(p\)-fold integrated empirical process with applications to statistical tests ⋮ Characterization of Brownian Gibbsian line ensembles ⋮ Some asymptotic results for the integrated empirical process with applications to statistical tests ⋮ Cramér-type moderate deviations for stationary sequences of bounded random variables ⋮ Sheep in wolf's clothing: using the least squares criterion for quantile estimation

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