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User:Mathstat/Partial distance correlation

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In statistics and in probability theory, partial distance correlation is a measure of statistical dependence between two random variables or two random vectors controlling for or removing the effect of one or more random variables.[1] This measure extends distance covariance and distance correlation[2] in a similar sense that partial correlation extends correlation. The random variables/vectors of interest take values in arbitrary, not necessarily equal dimension Euclidean space.

Definitions

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The sample partial distance covariance is defined in terms of orthogonal projections as follows.

U-centered distance matrix

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Inner Product

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Projections

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Partial Distance Correlation

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Population Coefficients

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Notes

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  1. ^ Székely, G. J. and Rizzo, M. L. (2014). "Partial Distance Correlation with Methods for Dissimilarities". Annals of Statistics. 42 (6): 2382–2412.{{cite journal}}: CS1 maint: multiple names: authors list (link) Reprint
  2. ^ Székely, G. J. Rizzo, M. L. and Bakirov, N. K. (2007). "Measuring and testing independence by correlation of distances". Annals of Statistics. 35 (6): 2769–2794. doi:10.1214/009053607000000505.{{cite journal}}: CS1 maint: multiple names: authors list (link)Reprint

References

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  • Székely, G. J. and Rizzo, M. L. (2009). "Brownian Distance Covariance". Annals of Applied Statistics. 3 (4): 1233–1303. doi:10.1214/09-AOAS312.{{cite journal}}: CS1 maint: multiple names: authors list (link) Reprint
  • Lyons, R. (2013). "Distance covariance in metric spaces". Annals of Probability. 41 (5): 3284–3305. reprint


Category:Statistical dependence Category:Statistical distance measures Category:Theory of probability distributions Category:Multivariate statistics Category:Covariance and correlation