Re: transformation of covariance matrix


In general, let ti (i=1, ..., p) be the rvs for which you have the covariance matrix.

Let sj = sj(t1, ..., tp), (j = 1,..., q) be q new variables which are transforms of the ti's.

Then approximately,

Cov(si,sj) ~ Sum[Sum[(dsi/dtk)*(dsj/dtl)*Cov(tk,tl)]],

where the sum is over j,l = 1, ..., p.

Just calculate the partial derivatives and plug it in.

Jack

Thank you very much for your reply, however, I don't know how to
calculate the dsi/dtk
and dsj/dtl in your reply.

I should describe my question more clear.
In my question, alpha, beta, C are parameters estimated from a probit
model.
alpha, beta and C, and mu and sigma are scalar, and not variable
(vectors)
in my question. so I don't know whether it's possible to get the
covariance
matrix of mu and sigma.

a numeric example:

The alpha, beta and C and their standard error is following:
Estimate Std. Error
alpha -4.1437788 1.34146006
beta 6.2306286 1.89954481
c 0.2408866 0.05225879

And the covariance matrix is:
alpha beta c
alpha 1.79951508 -2.51894315 -0.031737662
beta -2.51894315 3.60827049 0.038782941
c -0.03173766 0.03878294 0.002730981

Now,
mu = 0.665066
and
sigma = 0.1604975

Now, my question is whether it is possible to get covariance matrix of
mu and sigma from the above information.

Thanks again.

Regards,
Jinsong
.

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