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Graphical Comparison of High‐Dimensional Distributions
Author(s) -
Modarres Reza
Publication year - 2020
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12358
Subject(s) - mathematics , statistics , plot (graphics) , scale (ratio) , distribution (mathematics) , cumulative distribution function , econometrics , geography , probability density function , mathematical analysis , cartography
Summary We consider groups of observations inR dand present a simultaneous plot of the empirical cumulative distribution functions of the within and between interpoint distances to visualise and examine the equality of the underlying distribution functions of the observations. We provide several examples to illustrate how such plots can be utilised to envision and canvass the relationship between the two distributions under location, scale, dependence and shape changes. We suggest new statistics for testing the equality of k distributions and extend the simultaneous plots to visualise them. We compare the new statistics to existing tests based on the interpoint distances.