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Activity Number: 515 - Visualization for Distributions, Networks and Statistical Inference
Type: Contributed
Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Graphics
Abstract #301687 Presentation
Title: Graphical Comparison of High-Dimensional Distributions
Author(s): Reza Modarres*
Companies: George Washington University
Keywords: Homogeneity; Interpoint Distance; Graphical Comparison; High Dimension

We consider the within and between interpoint distances (IPDs) of two groups of observations in $\mathbb{R}^d$. We suggest a simultaneous plot of the empirical cumulative distribution functions of the IPDs to visualize and examine the equality of the underlying distribution functions of the observations. We provide several examples to illustrate how such plots can be utilized to envision and canvass the relationship between the two distributions under location shift, scale, shape, and dependence changes. We extend the simultaneous plots to compare $k>2$ distributions and suggest new statistics for testing the equality of $k$ distributions. We compare the new statistics to existing test statistics based on the IPDs under changes in location and scale.

Authors who are presenting talks have a * after their name.

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