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The limiting eigenvalue distribution of a multivariate F matrix. (English) Zbl 0606.62054
Let $$X_{ij}$$, $$Y_{ij}$$, $$i,j=1,2,..$$. be i.i.d. N(0,1) random variables and for positive integers p,m,n, let $$\bar X{}_ p=(X_{ij})$$, $$i=1,2,...,p$$; $$j=1,2,...,m$$, and $$\bar Y{}_ p=(Y_{ij})$$, $$i=1,2,...,p$$; $$j=1,2,...,n$$. Suppose further that $$p/m\to y>0$$ and p/n$$\to y'\in (0,)$$, as $$p\to \infty$$. Y. Q. Yin and P. R. Krishnaiah [J. Multivariate Anal. 13, 489-507 (1983; Zbl 0553.62018)] and Y. Q. Yin, Z. D. Bai and P. R. Krishnaiah [ibid. 13, 508-516 (1983; Zbl 0531.62018)] showed that the empirical distribution function of the eigenvalues of $(m^{-1}\bar X_ p\bar X^ T_ p)(n^{-1}\bar Y_ p\bar Y^ T_ p)^{-1}$ converges i.p. as $$p\to \infty$$ to a nonrandom d.f. In the present paper the limiting d.f. is derived.

##### MSC:
 62H10 Multivariate distribution of statistics
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