Work

Visualizing Multiple Quantile Plots

Year: 2012

Type: article

Abstract: Multiple-quantile plots provide a powerful graphical method for comparing the distributions of two or more populations. This article develops a method of visualizing triple-quantile plots and their associated confidence tubes, thus extending the notion of a quantile–quantile (QQ) plot to three dimensions. More specifically, we consider three independent one-dimensional random samples with corresponding quantile functions Q1, Q2, and Q3. The triple-quantile (QQQ) plot is then defined as the three-dimensional curve Q(p) = (Q1(p), Q2(p), Q3(p)), where 0 < p < 1. The empirical likelihood method is used to derive simultaneous distribution-free confidence tubes for Q. We apply our method to an economic case study of strike durations and to an epidemiological study involving the comparison of cholesterol levels among three populations. These data as well as the Mathematica code for computation of the tubes are available in the online supplementary materials.

Source: Journal of Computational and Graphical Statistics

DOI: 10.1080/10618600.2012.680865

Authors: Marko A. A. Boon, John H. J. Einmahl, Ian W. McKeague

Institutions: Eindhoven University of Technology, Tilburg University, Columbia University

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Institutes of Health, National Institute of General Medical Sciences

Award: Post-selection inference and trajectory analysis