## Probability Surveys

### Quantile coupling inequalities and their applications

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 28 November 2012

https://projecteuclid.org/euclid.ps/1354125785

Digital Object Identifier
doi:10.1214/12-PS198

Mathematical Reviews number (MathSciNet)
MR3007210

Zentralblatt MATH identifier
1307.62036

#### Citation

Mason, David M.; Zhou, Harrison H. Quantile coupling inequalities and their applications. Probab. Surveys 9 (2012), 439--479. doi:10.1214/12-PS198. https://projecteuclid.org/euclid.ps/1354125785

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