Translator Disclaimer
2012 Quantile coupling inequalities and their applications
David M. Mason, Harrison H. Zhou
Probab. Surveys 9(none): 439-479 (2012). DOI: 10.1214/12-PS198

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.

Citation

Download Citation

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

Information

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

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

Subjects:
Primary: 62E17
Secondary: 62B15, 62G05

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

JOURNAL ARTICLE
41 PAGES


SHARE
Vol.9 • 2012
Back to Top