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Mathematics > Statistics Theory

arXiv:1909.10140 (math)
[Submitted on 23 Sep 2019 (v1), last revised 28 Apr 2020 (this
version, v4)]

Title:A new coefficient of correlation

Authors:Sourav Chatterjee
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    Abstract: Is it possible to define a coefficient of correlation
    which is (a) as simple as the classical coefficients like
    Pearson's correlation or Spearman's correlation, and yet (b)
    consistently estimates some simple and interpretable measure of
    the degree of dependence between the variables, which is 0 if and
    only if the variables are independent and 1 if and only if one is
    a measurable function of the other, and (c) has a simple
    asymptotic theory under the hypothesis of independence, like the
    classical coefficients? This article answers this question in the
    affirmative, by producing such a coefficient. No assumptions are
    needed on the distributions of the variables. There are several
    coefficients in the literature that converge to 0 if and only if
    the variables are independent, but none that satisfy any of the
    other properties mentioned above.

Comments: 39 pages, 9 figures, 2 tables. To appear in J. Amer.
          Statist. Assoc. R package available at this https URL
Subjects: Statistics Theory (math.ST); Probability (math.PR)
MSC       62H20, 62H15
classes:
Cite as:  arXiv:1909.10140 [math.ST]
          (or arXiv:1909.10140v4 [math.ST] for this version)

Submission history

From: Sourav Chatterjee [view email]
[v1] Mon, 23 Sep 2019 03:31:42 UTC (473 KB)
[v2] Thu, 26 Sep 2019 02:22:00 UTC (473 KB)
[v3] Sat, 18 Jan 2020 06:29:23 UTC (553 KB)
[v4] Tue, 28 Apr 2020 21:55:04 UTC (554 KB)
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