Probability Surveys

Quantile coupling inequalities and their applications

David M. Mason and Harrison H. Zhou

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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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Probab. Surveys, Volume 9 (2012), 439-479.

First available in Project Euclid: 28 November 2012

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Zentralblatt MATH identifier

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 62B15: Theory of statistical experiments 62G05: Estimation

Quantile coupling large deviation KMT construction asymptotic equivalence function estimation


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

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