Energy statistics: A class of statistics based on distances
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...(2011), Vrac and Friederichs (2015), Mehrotra and Sharma (2016), and Cannon (2016), MBCn is not restricted to correcting a specified measure of joint dependence, such as Pearson or Spearman rank correlation, nor does it make strong stationarity assumptions about climate model temporal sequencing....
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"Energy statistics: A class of stati..." refers background in this paper
...See also historical comments on “Hoeffding-type inequalities” and their generalizations in Gneiting and Raftery (2007, Section 5.2)....
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...The energy score (see Gneiting and Raftery [15])....
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...(iv) The energy score (see Gneiting and Raftery, 2007)....
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...Applying formulas 3.3.2.1, p. 585, 2.2.4.24 p. 298 and 2.5.3.13 p. 387 of Prudnikov et al. (1986), we obtain A≔ Z Rd−1 dz2dz3…dzd ð1þz22þz23þ⋯þz2dÞðdþαÞ=2 ¼ 2π ðd−1Þ=2 Γ d−1 2 Z ∞ 0 xd−2 dx ð1þx2ÞðdþαÞ=2 ¼ πðd−1Þ=2Γ αþ1 2 Γ dþα 2 ; d da Z ∞ 0 1−cos au u1þα du ¼ aα−1 Z ∞ 0 sin v vα dv¼ aα−1…...
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