Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions

Fabian Dunker, Stephan Klasen, Tatyana Krivobokova

Publications: Contribution to journalArticlePeer Reviewed

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.
Original languageEnglish
Pages (from-to)4391-4415
Number of pages25
JournalElectronic Journal of Statistics
Volume13
Issue number2
DOIs
Publication statusPublished - 6 Nov 2019
Externally publishedYes

Austrian Fields of Science 2012

  • 101018 Statistics

Keywords

  • ESTIMATORS
  • GROWTH
  • Growth incidence curve
  • INCOME
  • MODELS
  • NONPARAMETRIC-ESTIMATION
  • SMOOTH QUANTILE
  • STATISTICAL-INFERENCE
  • quantile processes
  • simultaneous confidence bands
  • Quantile processes
  • Simultaneous confidence bands

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