Abstract
In this paper we suggest a simple way of constructing a robust non parametric bivariate contour based on the rotation of the univariate box-plot which does not necessarily have to use a bivariate generalization of the univariate depth measures. The suggested approach is based on the projection of bivariate data along the round angle. When the angle is a multiple of π/2 we obtain the traditional univariate boxplot referred to each variable. In all the other cases we obtain univariate boxplots which keep into account in a different way the correlation between the two original variables. We apply the suggested approach to some datasets and exploit the properties of the different choices of defining the inner region and the outer contour. The final result is a simple and easy to construct bivariate boxplot which enables to visualize the location, spread skewness and tails of the data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chaudhuri, P. (1996). On a geometric notion of quantiles for multivariate data. J. of the American Statistical Association, 91, 862–872.
Efron, B. (1965). The Convex Hull on a Random Set of Points, Biometrika, 52 331–343.
Green, P.J. and Silverman, B.W. (1994). Nonparametric Regression and Generalized Linear Models, Chapman & Hall, London.
Goldberg, K.M., and Iglewicz, B. (1992). Bivariate Extensions of the Boxplot, Technometrics, 34, 307–320.
Hyndman, R.J. (1996). Computing and Graphic Highest Density Regions, Applied Statistics, 46, 295–298.
Liu, R.Y., Parelius, J. M., and Singh, K. (1999). Multivariate Analysis by Data Depth: Descriptive Statistics, Graphics and Inference, Annals of statistics, 27, 783–840.
Rousseeuw, P.J., Ruts, I, and Tukey, W. (1999). The Bagplot: A Bivariate Boxplot, The American Statistician, 53, 382–387.
Rousseeuw, P.J., Leroy, A. (1997). Robust Regression and Outlier Detection, Wiley, New York.
Zani, S., Riani, M. and Corbellini, A. (1998). Robust Bivariate Boxpot and Multiple Outlier Detection, Computational Statistics and Data Analysis, 28 257–270.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Corbellini, A. (2002). Clockwise Bivariate Boxplots. In: Härdle, W., Rönz, B. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57489-4_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-57489-4_31
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1517-7
Online ISBN: 978-3-642-57489-4
eBook Packages: Springer Book Archive