Asymptotic expansions for distributions of latent roots in multivariate analysis
Asymptotic expansions are given for the distributions of latent roots of matrices in three multivariate situations. The distribution of the roots of the matrix S1(S1 + S2)-1, where S1 is Wm(n1, [Sigma], [Omega]) and S2 is Wm(n2, [Sigma]), is studied in detail and asymptotic series for the distribution are obtained which are valid for some or all of the roots of the noncentrality matrix [Omega] large. These expansions are obtained using partial-differential equations satisfied by the distribution. Asymptotic series are also obtained for the distributions of the roots of n-1S, where S in Wm(n, [Sigma]), for large n, and S1S2-1, where S1 is Wm(n1, [Sigma]) and S2 is Wm(n2, [Sigma]), for large n1 + n2.
Volume (Year): 6 (1976)
Issue (Month): 3 (September)
|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:jmvana:v:6:y:1976:i:3:p:369-391. 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: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.