User:Mathstat/Partial distance correlation
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
[edit]The sample partial distance covariance is defined in terms of orthogonal projections as follows.
U-centered distance matrix
[edit]Inner Product
[edit]Projections
[edit]Partial Distance Correlation
[edit]Population Coefficients
[edit]Notes
[edit]- ^ 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 - ^ 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
[edit]- 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
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Category:Statistical dependence Category:Statistical distance measures Category:Theory of probability distributions Category:Multivariate statistics Category:Covariance and correlation