nlminb with constraint

["John Pitchard" <johnpitchard@googlemail.com>]

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[1] + ...+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