The convergence of the empirical distribution of canonical correlation coefficients

نویسندگان

  • Yanrong Yang
  • Guangming Pan
چکیده

Suppose that {Xjk, j = 1, · · · , p1; k = 1, · · · , n} are independent and identically distributed (i.i.d) real random variables with EX11 = 0 and EX 2 11 = 1, and that {Yjk, j = 1, · · · , p2; k = 1, · · · , n} are i.i.d real random variables with EY11 = 0 and EY 2 11 = 1, and that {Xjk, j = 1, · · · , p1; k = 1, · · · , n} are independent of {Yjk, j = 1, · · · , p2; k = 1, · · · , n}. This paper investigates the canonical correlation coefficients r1 ≥ r2 ≥ · · · ≥ rp1 , whose squares λ1 = r 1, λ2 = r 2, · · · , λp1 = r p1 are the eigenvalues of the matrix Sxy = A −1 x AxyA −1 y A T xy, where Ax = 1 n n ∑ k=1 xkx T k , Ay = 1 n n ∑ k=1 yky T k , Axy = 1 n n ∑

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تاریخ انتشار 2012