[R] A stupid question on F-statistics
f0z6305 at labs.tamu.edu
Thu Jan 23 22:56:02 CET 2003
Just a stupid question confused me for a long time.
Now suppose p_dim random vector x (column vector) are from
a multivariate normal N(mu, Sigma).
Given a sample size n, (x1, x2, ....., xn),
and the sample mean is x_bar, sample covariance is S.
I can infer that
n(x_bar - mu)'*inverse(S)*(x_bar - mu) is distributed as F(p, n-p), and for
a new observation vector x,
(x - mu)'*inverse(S)*(x - mu) is distributed as F(p, n-p).
So why the follow statistics T is distributed as
T = (x - x_bar)'*inverse(S)*(x - x_bar)
Thanks so much for pointing me the way to solve it out.
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