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Re: st: Standard error of the forecast and multivariate regression


From   Gillian.Frost@hsl.gsi.gov.uk
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Standard error of the forecast and multivariate regression
Date   Thu, 31 Oct 2013 12:23:56 +0000

Hello,

I took Nick's advice and contacted tech support.  I thought that I would 
post their response just to close off this thread.

******************************************************************************************************************
The standard errors of forecast are only defined for models fitted by
ordinary least square for which the estimated covariance matrix is
p-by-p of the form {V = s^2 (X'WX)^-1}, where p is the number of
predictors and s^2 is the sample standard error. Then, the std. err. of
forecast for observation x_j is s*sqrt{1 + x_j (X'X)^-1 x_j'}.  This is
not the case in multivariate regression with (Y_i), i=1..q>1 dependent
variables where the estimated covariance is pq-by-pq and the forecast
errors cannot be single numbers but q-by-q matrices. Thus, the -predict-
command cannot report and save them as variables. Similar is the case
with the score option.

In principle, the forecast correlation error between Y_i and Y_k is of
the form s_{ik}*sqrt{1 + x_j (X'X)^-1 x_j'}. With little more work these
can be calculated from the estimated matrices -e(V)- and -e(Sigma)-
reported by -mvreg-; s_{ik} are the components of -e(Sigma)-. 
******************************************************************************************************************

I'm afraid it's beyond my skills to try to calculate the forecast 
correlation error, so I'll probably leave this train of thought for now.

Regards,

Gillian




From:   Nick Cox <njcoxstata@gmail.com>
To:     "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Date:   30/10/2013 10:21
Subject:        Re: st: Standard error of the forecast and multivariate 
regression
Sent by:        owner-statalist@hsphsun2.harvard.edu



I couldn't answer your question, so I just commented, and can't add to
my comment. I would take this to tech support if no StataCorp person
comments.
Nick
njcoxstata@gmail.com


On 29 October 2013 16:52,  <Gillian.Frost@hsl.gsi.gov.uk> wrote:
> Hello all,
>
> This is probably a statistical question, but I wondered if anyone could
> help me.
>
> I was wondering if anyone could provide me with a reason why it is not
> possible to generate the standard error of the forecast using -predict
> newvar, stdf- after multivariate regression using -mvreg- ?
> I read somewhere in the help files (although I can't see where now) that
> the -stdf- option can only be used for a regression where the score can 
be
> calculated using -predict newvar, score-.  Now -mvreg- doesn't allow the
> score option of -predict-, which I'm guessing is why stdf cannot be
> specified.  However this doesn't really explain why the score option is
> not valid for multivariate regression.  Can anyone help?
>
> Is this specific to Stata, or would this be the same in whichever
> statistical package you were using?  I'm just wondering if I could turn 
to
> R or some other programme.
>
> I'd be grateful for any insights.
>
> Many thanks,
>
> Gillian
>
>
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