Smooth depth contours characterize the underlying distribution

Smooth depth contours characterize the underlying distribution

The Tukey depth is an innovative concept in multivariate data analysis. It can be utilized to extend the univariate order concept and advantages to a multivariate setting. While it is still an open question as towhether the depth contours uniquely determine the underlying distribution, some positive answers have been provided. We extend these results to distributions with smooth depth contours,...

Halfspace Depth and Regression Depth Characterize the empirical Distribution

For multivariate data, the halfspace depth function can be seen as a natural and affine equivariant generalization of the univariate empirical cdf. For any multivariate data set, we show that the resulting halfspace depth function completely determines the empirical distribution. We do this by actually reconstructing the data points from the depth contours. The data need not be in general posit...

Subjective contours and apparent depth.

Schumann (1904) investigated the physical parameters which affect the perception of contour. He reported that for a contour to be perceived the prerequisite was some relatively abrupt local change in brightness or color. In the course of these investigations, however, he noted that under certain favorable conditions contours could be made to appear in areas of the visual field where the physica...

Proximity graph depth, depth contours, and a new multimodal median

We propose proximity graph depth as a class of depth functions, based on the minimum path length along proximity graph edges to the convex hull of a point set. We analyze the characteristics of several proximity graph depth functions both theoretically and experimentally, define depth contours enclosing regions of increasing depth, and present algorithms for calculating depth values in a point ...

Computing Depth Contours with Graphics Hardware