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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.

62-09 Graphical methods in statistics (MSC2010)
62-07 Data analysis (statistics) (MSC2010)
Full Text: DOI
[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.
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