Re: Covariance with bounds in leasqr

[Olaf Till]

On Wed, Mar 21, 2012 at 06:31:51PM -0300, Pablo wrote:
> Hi everyone,
>   I've been intrigued by a detail in leasqr (from Octave-Forge) for
> a while. In the function's documentation it's stated that "If
> constraints (or bounds) are set, returned guesses of corp, covp, and
> Z are generally invalid, even if no constraints are active for the
> final parameters".
> 
>   I wonder why is that, particularly for covp (it's usually the most
> useful for me). Unfortunately, I don't seem to have access to the
> reference given (Bard) so I can't check if that's mentioned there.
> Also, a few web searches didn't give me any clue.
>   I'm familiar with the way the covariance of the parameters is
> calculated for a linear fit, and as far as I can see it's
> essentially the same for leasqr.
> 
>   Could anyone give me some pointers as to why that statement is
> true? Any references or links to help me understand it would also be
> highly appreciated.
> 
>   Best Regards,
>     Arnoques

This is not specific to leasqr. Roughly speaking, the covariance
matrix of estimated parameters is a guess on how estimated parameters
change due to random in the input data. But if they change, they might
hit (and so are influenced by) a constraint, even if the constraint is
not active for the current estimation of parameters. This prevents an
easy estimation of the covariance matrix of parameters from (possibly
estimated) (co)variance of input data.

Olaf

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