On the uniqueness of distance covariance
Distance covariance and distance correlation are non-negative real numbers that characterize the independence of random vectors in arbitrary dimensions. In this work we prove that distance covariance is unique, starting from a definition of a covariance as a weighted L2 norm that measures the distance between the joint characteristic function of two random vectors and the product of their marginal characteristic functions. Rigid motion invariance and scale equivariance of these weighted L2 norms imply that the weight function of distance covariance is unique.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 82 (2012)
Issue (Month): 12 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2278-2282. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.