Re: st: Nonlinear regression and constraints

["Erik �. S�rensen" <sameos@gmail.com>]

On 29. jun. 2005, at 08.49, Daniel Schneider wrote:
> Without going to much into detail: my parameters are percentages. They
> can only range from 0 to 1. There may be a better solution (i.e. a
> solution that better fits the data) beyond 1, BUT, as I said, by
> definition they cannot be above 1 (or below 0). So the best solution
> that is possible has to be between 0 and 1.
I think the easiest way to do this is to define a function g:R-> (0,1),
and then where you want to estimate a parameter \theta \in (0,1),
you instead make the transformation of variables

   \theat = exp(x)/(1+exp(x)).

So stata optimises to find an x \in R, but you know that the estimate  
of your parameter is \theta^*=exp(x^*)/(1+exp(x^*)). You can use  
asymptotic theory to find the standard errors of this transformation.  
Or you can estimate first with this method and then reestimate with  
starting points close to the estimates and hope that it converges to  
the same estimates instead of going off out of the allowed parameter  
space.

I'm not sure it is a good idea to try to adopt to the possibility  
that \theta=0 or \theta=1, at least all standard asymptotic  
distribution theory would break down at the limits of the parameter  
space.

best regards,
Erik



--
Erik �. S�rensen, dept of Econ., Norwegian School of Economics




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