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Re: Covariance with bounds in leasqr


From: CdeMills
Subject: Re: Covariance with bounds in leasqr
Date: Thu, 22 Mar 2012 01:32:20 -0700 (PDT)

Olaf Till-2 wrote
> 
> 
> 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.
> 
> 
I have to disagree with this statement. The covariance matrix is usually
computed from first-order development around the operating point. It permits
A.O. to determine confidence intervals on the estimated parameters value, to
assert wether or not values are significantly different from zero and so on.

The limit is that this first order development must be valid. Otherwise you
must include more terms and higher order statistics. I think that the doc
should emphasize about it by not speaking about covariance, but first-order
approximation of the covariance matrix.

Regards

Pascal

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