Wed Apr 9 13:51:00 CEST 2008

```Hi Spencer,

Sorry for not producing code as a worked example.

Here's an example:
==================================
# setting the seed number
set.seed(0)
# creating a correlation matrix
corr <- diag(5)
corr[lower.tri(corr)] <- 0.5
corr[upper.tri(corr)] <- 0.5

# Data for the minimisation
mat <- rmvnorm(10000, mean=c(3, -20, -10, 3, 2), sd=c(0.1, 15, 4,
0.15, 0.8), cov=corr)

obj.fun <- function(opt, mat) {
opt <- c(opt, 1-sum(opt))
LinearComb <- mat%*%opt
obj <- -min(LinearComb)
obj
}

opt <- nlminb(rep(0,4), lower=rep(-3, 4), upper=rep(3, 4), obj.fun, mat=mat)
opt.x <- opt\$parameters
opt.x <- c(opt.x, 1-sum(opt.x))

# using vcov.nlminb from the MASS library to obtain the covariance matrix
vcov.nlminb(opt)
====================================

I have a variance-covariance matrix for 4 of the elements in the
vector but not the last component. How would I go about getting the
entire variance-covariance matrix?

Thanks in advance for any help.

Regards,
John

On 09/04/2008, Spencer Graves <spencer.graves at pdf.com> wrote:
>     Have you considered optimizing over x1 = x[1:(length(x)-1]?   You could feed a wrapper function 'f2(x1, ...)' that computes xFull = c(x1, 1-sum(x1)) and feeds that to your 'fn'.
>     If this makes sense, great.  Else, if my answer is not useful, be so kind as to PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
>     Spencer
>
> John Pitchard wrote:
>
> >
> >  Dear All,
> >
> > I wanted to post some more details about the query I sent to s-news last
> > week.
> >
> > I have a vector with a constraint. The constraint is that the sum of the
> > vector must add up to 1 - but not necessarily positive, i.e.
> >
> > x[n] <- 1 -(x + ...+x[n-1])
> >
> > I perform the optimisation on the vector x such that
> >
> > x <- c(x, 1-sum(x))
> >
> > In other words,
> >
> > fn <- function(x){
> >  x <- c(x, 1 - sum(x))
> >  # other calculations here
> > }
> >
> > then feed this into nlminb()
> >
> > out <- nlminb(x, fn)
> > out.x <- out\$parameters
> > out.x <- c(out.x, 1 - sum(out.x))
> > out.x
> >
> > I would like to calculate standard errors for each of the components of x.
> > Is this possible by outputing the Hessian matrix? Furthermore, how would I
> > calculate this for the last component (if this is indeed possible) which has
> > the restriction (i.e. 1-sum(out.x))?
> >
> > Any help would be much appreciated.
> >
> > Regards,
> > John
> >
> >        [[alternative HTML version deleted]]
> >
> > ______________________________________________
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