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| Abstract |
We shall give in this note a simple Proof of a SAKAMOTO-CRAIG's theorem concerning the independence of two statistics $ q_1 = (xA,x) $and $ q_2 = (xB,x) $ $ (A = A', B = B') $, where $ x $ is an $ n $...-dimensional random vector with the normal distribution whose covariance matrix is $ V $. Especially we prove here $ AVB = 0 $ is necessary if we assume $ E({q_1}^i{q_2}^j) = E({q_1}^i)E({q_2}^j) $, $ i,j = 1,2 $.show more
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