A multivariate generalization of quantile–quantile plots

George S. Easton, Robert McCulloch

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

In this article we present a multivariate generalization of quantile-quantile (Q–Q) plots. Like univariate Q–Q plots, these plots are useful for examining the distributional shape of multivariate point clouds. These plots are based on finding a matching between the points of the data set whose shape is being examined and a reference sample. Graphical displays of how well the point clouds match are then developed. The reference sample used as the basis for comparison is typically derived from a random sample from a known multivariate distribution. The approach presented in this article is both a direct extension of the usual univariate Q–Q plot and truly multivariate in nature. It is truly multivariate in that the displays we develop show different aspects of one multivariate comparison between the data and the reference sample. This is unlike most generalizations of Q–Q plots to the multivariate case, which are based on making standard univariate Q–Q plots after some function of the multivariate observations has been used to reduce the dimension of the problem. Our method is also not tied to any specific reference distribution such as the multivariate normal. Furthermore, because it is truly multivariate, it is capable of uncovering certain kinds of features in the data that can be very difficult to detect using standard approaches.

Original languageEnglish (US)
Pages (from-to)376-386
Number of pages11
JournalJournal of the American Statistical Association
Volume85
Issue number410
DOIs
StatePublished - 1990
Externally publishedYes

Fingerprint

Quantile
Univariate
Point Cloud
Generalization
Graphical Display
Multivariate Normal
Multivariate Distribution
Display

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

A multivariate generalization of quantile–quantile plots. / Easton, George S.; McCulloch, Robert.

In: Journal of the American Statistical Association, Vol. 85, No. 410, 1990, p. 376-386.

Research output: Contribution to journalArticle

@article{7d1dba98dfbf4f219cc6931bc10a2de2,
title = "A multivariate generalization of quantile–quantile plots",
abstract = "In this article we present a multivariate generalization of quantile-quantile (Q–Q) plots. Like univariate Q–Q plots, these plots are useful for examining the distributional shape of multivariate point clouds. These plots are based on finding a matching between the points of the data set whose shape is being examined and a reference sample. Graphical displays of how well the point clouds match are then developed. The reference sample used as the basis for comparison is typically derived from a random sample from a known multivariate distribution. The approach presented in this article is both a direct extension of the usual univariate Q–Q plot and truly multivariate in nature. It is truly multivariate in that the displays we develop show different aspects of one multivariate comparison between the data and the reference sample. This is unlike most generalizations of Q–Q plots to the multivariate case, which are based on making standard univariate Q–Q plots after some function of the multivariate observations has been used to reduce the dimension of the problem. Our method is also not tied to any specific reference distribution such as the multivariate normal. Furthermore, because it is truly multivariate, it is capable of uncovering certain kinds of features in the data that can be very difficult to detect using standard approaches.",
author = "Easton, {George S.} and Robert McCulloch",
year = "1990",
doi = "10.1080/01621459.1990.10476210",
language = "English (US)",
volume = "85",
pages = "376--386",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "410",

}

TY - JOUR

T1 - A multivariate generalization of quantile–quantile plots

AU - Easton, George S.

AU - McCulloch, Robert

PY - 1990

Y1 - 1990

N2 - In this article we present a multivariate generalization of quantile-quantile (Q–Q) plots. Like univariate Q–Q plots, these plots are useful for examining the distributional shape of multivariate point clouds. These plots are based on finding a matching between the points of the data set whose shape is being examined and a reference sample. Graphical displays of how well the point clouds match are then developed. The reference sample used as the basis for comparison is typically derived from a random sample from a known multivariate distribution. The approach presented in this article is both a direct extension of the usual univariate Q–Q plot and truly multivariate in nature. It is truly multivariate in that the displays we develop show different aspects of one multivariate comparison between the data and the reference sample. This is unlike most generalizations of Q–Q plots to the multivariate case, which are based on making standard univariate Q–Q plots after some function of the multivariate observations has been used to reduce the dimension of the problem. Our method is also not tied to any specific reference distribution such as the multivariate normal. Furthermore, because it is truly multivariate, it is capable of uncovering certain kinds of features in the data that can be very difficult to detect using standard approaches.

AB - In this article we present a multivariate generalization of quantile-quantile (Q–Q) plots. Like univariate Q–Q plots, these plots are useful for examining the distributional shape of multivariate point clouds. These plots are based on finding a matching between the points of the data set whose shape is being examined and a reference sample. Graphical displays of how well the point clouds match are then developed. The reference sample used as the basis for comparison is typically derived from a random sample from a known multivariate distribution. The approach presented in this article is both a direct extension of the usual univariate Q–Q plot and truly multivariate in nature. It is truly multivariate in that the displays we develop show different aspects of one multivariate comparison between the data and the reference sample. This is unlike most generalizations of Q–Q plots to the multivariate case, which are based on making standard univariate Q–Q plots after some function of the multivariate observations has been used to reduce the dimension of the problem. Our method is also not tied to any specific reference distribution such as the multivariate normal. Furthermore, because it is truly multivariate, it is capable of uncovering certain kinds of features in the data that can be very difficult to detect using standard approaches.

UR - http://www.scopus.com/inward/record.url?scp=0000012684&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000012684&partnerID=8YFLogxK

U2 - 10.1080/01621459.1990.10476210

DO - 10.1080/01621459.1990.10476210

M3 - Article

AN - SCOPUS:0000012684

VL - 85

SP - 376

EP - 386

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 410

ER -