Open Access
2012 Quantile coupling inequalities and their applications
David M. Mason, Harrison H. Zhou
Probab. Surveys 9: 439-479 (2012). DOI: 10.1214/12-PS198


This is partly an expository paper. We prove and highlight a quantile inequality that is implicit in the fundamental paper by Komlós, Major, and Tusnády [31] on Brownian motion strong approximations to partial sums of independent and identically distributed random variables. We also derive a number of refinements of this inequality, which hold when more assumptions are added. A number of examples are detailed that will likely be of separate interest. We especially call attention to applications to the asymptotic equivalence theory of nonparametric statistical models and nonparametric function estimation.


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David M. Mason. Harrison H. Zhou. "Quantile coupling inequalities and their applications." Probab. Surveys 9 439 - 479, 2012.


Published: 2012
First available in Project Euclid: 28 November 2012

zbMATH: 1307.62036
MathSciNet: MR3007210
Digital Object Identifier: 10.1214/12-PS198

Primary: 62E17
Secondary: 62B15 , 62G05

Keywords: ‎asymptotic ‎equivalence , Function estimation , KMT construction , large deviation , Quantile coupling

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.9 • 2012
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