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MathGroup Archive 2004

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Re: Obtaining Standard Errors when using FindMinimum in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47577] Re: Obtaining Standard Errors when using FindMinimum in Mathematica
  • From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
  • Date: Fri, 16 Apr 2004 05:21:10 -0400 (EDT)
  • References: <c5lg8d$c0g$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Mathematica is behaving correctly. The location of the minimum of a function
is a point not a volume, unless the function is constant over some finite
volume around the minimum in which case Mathematica ignores that fact (but
might give you warning messages).

What you should do is to evaluate the Hessian matrix (matrix of second
derivatives) at the minimum, whose inverse matrix gives you the covariance
matrix about the minimum. If you diagonalise the covariance matrix it will
give you the principal axes and radii of the error volume you seek. However,
there is still an overall scale size for the error volume to be determined.
This depends on how accurately your function values are known in the first
place, which depends on the noise level in your data.

Steve Luttrell

"JoshW" <wimpeyjs at hotmail.com> wrote in message
news:c5lg8d$c0g$1 at smc.vnet.net...
> Is this possible?  I am using FindMinimum to estimate parameters by
> minimizing the negative log likelihood function....Just like you would
> do for maximum likelihood.  Mathematica only spits out parameter
> estimates and no SEs or confidence intervals.
>
> Any help would be much appreciated.
>


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