Abstract
Zani et al. (1997) suggested a simple way of constructing a bivariate boxplot based on convex hull peeling and B-spline smoothing. This approach leads to define a natural, smooth and completely non parametric region in ℝ 2 which retains the correlation in the data and adapts to differing spread in the various directions. In this paper we initially consider some variations of this method. The proposed approach shows some advantages with respect to that suggested by Goldberg and Iglewicz (1992), because we do not need to estimate either the standard deviations of the two variables or a correlation measure. Furthermore we also show how, in presence of p-dimensional data, the data visualization method based on the construction of the scatterplot matrix with superimposed bivariate boxplots in each diagram can become a very useful tool for the detection of multivariate outliers, the analysis of multivariate transformations and more generally for the ordering of multidimensional data.
This is a preview of subscription content, log in via an institution to check access.
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
ATKINSON, A.C. (1994): Fast very robust methods for the detection of multiple outliers, JASA, 89, 1329–1339.
BARNETT, V. (1976): The ordering of multivariate data, (with discussion), JRSS, Series A, 139, 318–339.
BARNETT, V. and LEWIS, T. (1994): Outliers in Statistical Data, 3rd edn., Wiley, New York.
BEBBINGTON, A.C. (1978): A method of bivariate trimming for robust estimation of the correlation coefficient. Appl. Statist., 27, 221–226.
EILERS, P.H.C. and MARX, B.D. (1996): Flexible Smoothing with B-splines and Penalties, Statistical Science, 11, 89–121.
GOLDBERG, K.M. and IGLEWICZ, B. (1992): Bivariate extensions of the box-plot, Technometrics, 34, 307–320.
HADI, A.S. (1992): Identifying multiple outliers in multivariate data, JRSSB, 54, 761–771.
HADI, A.S. (1992): Identifying multiple outliers in multivariate data, JRSSB, 54, 761–771.
RIANI, M. and ATKINSON, A.C., (1997): A Unified Approach to Multivariate Transformations and Multiple Outlier Detection, mimeo, London School of Economics and Political Science.
RUTS, I. and ROUSSEEUW (1996): Computing Depth Contours of Bivariate Point Clouds, Computational Statistics and Data Analysis, 23, 153–168.
ROUSSEEUW, P.J. and LEROY, A. (1987): Robust Regression and Outlier Detection, Wiley, New York.
SMALL, C.G. (1990): A survey of multidimensional medians, Intern. Stat. Rev., 58, 263–277.
VENABLES, W.N. and RIPLEY, B.D. (1994): Modern Applied Statistics with S-PLUS, Springer Verlag, Berlin.
ZANI, S. (1996): Measures of Quality of Life, (in italian), Franco Angeli, Milano.
ZANI S., RIANI, M. and CORBELLINI, A. (1997): Robust Bivariate Boxplots and Multiple Outlier Detection, submitted for publication to Computational Statistics and Data Analysis.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Riani, M., Zani, S., Corbellini, A. (1998). Robust Bivariate Boxplots and Visualization of Multivariate Data. In: Balderjahn, I., Mathar, R., Schader, M. (eds) Classification, Data Analysis, and Data Highways. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72087-1_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-72087-1_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63909-1
Online ISBN: 978-3-642-72087-1
eBook Packages: Springer Book Archive