Functional Forms of Characteristic Functions and Characterizations of Multivariate DistributionsYasuko Chikuse Econometric Theory, 1990, vol. 6, issue 04, pages 445-458 Abstract: During the Oxford Conference of the Econometric Society in 1936, Ragnar Frisch proposed a problem of characterization of distributions based on the property of linear regression of one linear function of random variables on the other. This problem has been solved, partially by Allen [1], and then completely by Rao [24,25], Fix [7], and Laha [13] relaxing the conditions imposed on the component random variables. The purpose of this paper is to solve the above mentioned problem for the multivariate case, characterizing multivariate distributions based on the multivariate linear regression of one linear function of not necessarily i.i.d. random vectors with matrix coefficients on the other. We make some mild assumptions concerning the component random vectors and the related constant matrices. It is shown that the property of multivariate linear regression yields a system of partial differential equations (p.d.e.'s) satisfied by the characteristic functions of the component random vectors. A general solution of this system of p.d.e.'s is given by certain functional forms. Special cases of the general solution give characterizations of the and the multivariate semistable laws, and a method is presented to characterize the multivariate stable laws. Date: 1990 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:6:y:1990:i:04:p:445-458_00 Access Statistics for this article More articles in Econometric Theory from Cambridge University Press |
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