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-   -   Third moments matrix, Please. (http://mymathforum.com/linear-algebra/33043-third-moments-matrix-please.html)

 karoon January 8th, 2013 01:09 AM

Third moments matrix, Please.

Matrix A =
x11 x12 x13 x14 x15
x21 x22 x23 x24 x25
x31 x32 x33 x34 x35
Then I need to find matrix of second moments and third moments, so I did

Matrix B =
x11-?1 x12-?1 x13-?1 x14-?1 x15-?1
x21-?2 x22-?2 x23-?2 x24-?2 x25-?2
x31-?3 x32-?3 x33-?3 x34-?3 x35-?3

Since variance-covariance matrix = ?(xi-?i) (xj-?j), therefore second moments matrix can be calculated as:
M2 = B.B' which is 3 by 3 matrix
This computation is fine for me, however, the third moments which can be calculated as:
M3 = ?(xi-?i) (xj-?j) (xk-?k) or
M3 = B.B' ? B'
The answer should be a matrix 3 by 9 or n by n^2, but I couldn’t do that.
I used the command in Matlab such as
1. M3=kron((B*transpose(B)),transpose(B))
Or 2.1 Give C = B*transpose(B), then,
2.2 M3=kron (C,transpose(B))
But the answer is a matrix 15 by 9 which I think it is incorrect.

It may be an easy question for all you guys but it's very difficult for me.