Summary:
We describe depth–based graphical displays that show the interdependence of multivariate distributions. The plots involve one–dimensional curves or bivariate scatterplots, so they are easier to interpret than correlation matrices. The correlation curve, modelled on the scale curve of Liu et al. (1999), compares the volume of the observed central regions with the volume under independence. The correlation DD–plot is the scatterplot of depth values under a reference distribution against depth values under independence. The area of the plot gives a measure of distance from independence. Correlation curve and DD-plot require an ‘independence’ model as a baseline: Besides classical parametric specifications, a nonparametric estimator, derived from the randomization principle, is used. Combining data depth and the notion of quadrant dependence, quadrant correlation trajectories are obtained which allow simultaneous representation of subsets of variables. The properties of the plots for the multivariate normal distribution are investigated. Some real data examples are illustrated.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
*This work was completed with the support of “Ca’ Foscari” University.
Rights and permissions
About this article
Cite this article
Romanazzi*, M. Data depth and correlation. Allgemeines Statistisches Arch 88, 191– 214 (2004). https://doi.org/10.1007/s101820400168
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s101820400168