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2019 Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions
Fabian Dunker, Stephan Klasen, Tatyana Krivobokova
Electron. J. Statist. 13(2): 4391-4415 (2019). DOI: 10.1214/19-EJS1628

Abstract

Ratios of medians or other suitable quantiles of two distributions are widely used in medical research to compare treatment and control groups or in economics to compare various economic variables when repeated cross-sectional data are available. Inspired by the so-called growth incidence curves introduced in poverty research, we argue that the ratio of quantile functions is a more appropriate and informative tool to compare two distributions. We present an estimator for the ratio of quantile functions and develop corresponding simultaneous confidence bands, which allow to assess significance of certain features of the quantile functions ratio. Derived simultaneous confidence bands rely on the asymptotic distribution of the quantile functions ratio and do not require re-sampling techniques. The performance of the simultaneous confidence bands is demonstrated in simulations. Analysis of expenditure data from Uganda in years 1999, 2002 and 2005 illustrates the relevance of our approach.

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Fabian Dunker. Stephan Klasen. Tatyana Krivobokova. "Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions." Electron. J. Statist. 13 (2) 4391 - 4415, 2019. https://doi.org/10.1214/19-EJS1628

Information

Received: 1 November 2018; Published: 2019
First available in Project Euclid: 6 November 2019

zbMATH: 07136620
MathSciNet: MR4028510
Digital Object Identifier: 10.1214/19-EJS1628

Subjects:
Primary: 62G15
Secondary: 62G30

JOURNAL ARTICLE
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Vol.13 • No. 2 • 2019
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