×

zbMATH — the first resource for mathematics

Positions and QQ plots. (English) Zbl 1100.62502
Summary: Quantile–quantile (QQ) plots for comparing two distributions are constructed by matching like-positioned values (i.e., quantiles) in the two distributions. These plots can reveal outliers, differences in location and scale, and other differences between the distributions. A particularly useful application is comparing residuals from an estimated linear model to the normal. A robust estimate, such as the Sen–Theil estimate, of the regression line is important. Extensions to two-dimensional QQ plots are presented, relying on a particular notion of multivariate position.

MSC:
62-09 Graphical methods in statistics (MSC2010)
62-07 Data analysis (statistics) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Barnett, V. (1975). Probability plotting methods and order statistics. Appl. Statist. 24 95–108.
[2] Chakraborty, B. (2001). On affine equivariant multivariate quantiles. Ann. Inst. Statist. Math. 53 380–403. · Zbl 1027.62035
[3] Chaudhuri, P. (1996). On a geometric notion of quantiles for multivariate data. J. Amer. Statist. Assoc. 91 862–872. · Zbl 0869.62040
[4] Cleveland, W. S. (1993). Visualizing Data . Hobart Press, Summit, NJ.
[5] Cook, R. D. and Weisberg, S. (1997). Graphics for assessing the adequacy of regression models. J. Amer. Statist. Assoc. 92 490–499. · Zbl 0890.62051
[6] Koltchinskii, V. I. (1997). \(M\)-estimation, convexity and quantiles. Ann. Statist. 25 435–477. · Zbl 0878.62037
[7] Liu, R. Y., Parelius, J. M. and Singh, K. (1999). Multivariate analysis by data depth: Descriptive statistics, graphics and inference. Ann. Statist. 27 783–858. · Zbl 0984.62037
[8] Marden, J. I. (1998). Bivariate QQ-plots and spider web plots. Statist. Sinica 8 813–826. · Zbl 0915.62057
[9] Möttönen, J., Oja, H. and Tienari, J. (1997). On the efficiency of multivariate spatial sign and rank tests. Ann. Statist. 25 542–552. · Zbl 0873.62048
[10] Rousseeuw, P. J. and Leroy, A. M. (1987). Robust Regression and Outlier Detection . Wiley, New York. · Zbl 0711.62030
[11] Rousseeuw, P. J., Ruts, I. and Tukey, J. W. (1999). The bagplot: A bivariate boxplot. Amer. Statist. 53 382–387.
[12] Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall’s tau. J. Amer. Statist. Assoc. 63 1379–1389. · Zbl 0167.47202
[13] Serfling, R. (2002). Quantile functions for multivariate analysis: Approaches and applications. Statist. Neerlandica 56 214–232. · Zbl 1076.62054
[14] Small, C. G. (1990). A survey of multidimensional medians. Internat. Statist. Rev. 58 263–277.
[15] Theil, H. (1950). A rank-invariant method of linear and polynomial regression analysis. I. Nederl. Akad. Wetensch. Proc. 53 386–392. · Zbl 0036.21601
[16] Visuri, S., Ollila, E., Koivunen, V., Möttönen, J. and Oja, H. (2003). Affine equivariant multivariate rank methods. J. Statist. Plann. Inference 114 161–185. · Zbl 1011.62053
[17] Wilk, M. B. and Gnanadesikan, R. (1968). Probability plotting methods for the analysis of data. Biometrika 55 1–17.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.