Visualizing multiple quantile plots

Marko A. A. Boon; John H. J. Einmahl; Ian W. McKeague

doi:10.1080/10618600.2012.680865

Visualizing multiple quantile plots

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

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

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 threedimensional 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. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Original language	English
Pages (from-to)	69-78
Journal	Journal of Computational and Graphical Statistics
Volume	22
Issue number	1
DOIs	https://doi.org/10.1080/10618600.2012.680865
Publication status	Published - 2013
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Confidence region
Empirical likelihood
Three-sample comparison

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title = "Visualizing multiple quantile plots",

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 threedimensional 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. {\textcopyright} 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.",

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T1 - Visualizing multiple quantile plots

AU - Boon, Marko A. A.

AU - Einmahl, John H. J.

AU - McKeague, Ian W.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2013

Y1 - 2013

N2 - 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 threedimensional 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. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

AB - 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 threedimensional 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. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

KW - Confidence region

KW - Empirical likelihood

KW - Three-sample comparison

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DO - 10.1080/10618600.2012.680865

M3 - RGC 21 - Publication in refereed journal

C2 - 24465124

SN - 1061-8600

VL - 22

SP - 69

EP - 78

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

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ER -

Visualizing multiple quantile plots

Abstract

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Research Keywords

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