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发帖数: 39 | 1 S is the sample covariance matrix of a random vector X.
From singular value decomposition,
S=UDU'
Partition the columns of U as (U1,U2).
W is the sample covariance matrix of vec(S), that is, the sample fourth-
moments of the random vector X.
The singular value decomposition of W is
W=AGA'
Hence, the inverse of W is Winv= A(G^-1)A'.
Define
kx as kronecker product,
and define two quadratic forms
L1=y'(U2'kxU2')Winv(U2kxU2)y = y'(U2'kxU2')A(G^-1)A'(U2kxU2)y
L2=y'(U2'kxU2')(G^-1)(U2kxU2)y
The questi |
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