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https://issues.apache.org/jira/browse/MATH-784?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Sébastien Brisard updated MATH-784:
-----------------------------------
Attachment: SyntheticDataLinear.java
Attached a new version of the MC simulation, whith a linear model y = a[0] +
a[1] * x, and only 3 observation points x[0] = 0.333, x[1] = 0.666 and x[2] =
1.0. It looks like in that case, the two estimator differ quite significantly,
and in fact, the simple one (unweighted square root of the diagonal
coefficients) is a much better estimator of the sd on the parameters.
It comes out as a surprise, because it contradicts formulas (34) and (35) in
[MathWorld|http://mathworld.wolfram.com/LeastSquaresFitting.html]. Also, the
standard deviation on the parameters in [NIST
StRD|http://www.itl.nist.gov/div898/strd/general/dataarchive.html] is computed
with the other formula.
> Javadoc of AbstractLeastSquaresOptimizer.guessParametersErrors() is too vague
> -----------------------------------------------------------------------------
>
> Key: MATH-784
> URL: https://issues.apache.org/jira/browse/MATH-784
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 3.0
> Reporter: Sébastien Brisard
> Assignee: Sébastien Brisard
> Labels: javadoc, optimization
> Fix For: 3.1
>
> Attachments: SyntheticData.java, SyntheticDataLinear.java
>
>
> This bug report follows a recent discussion available
> [here|http://mail-archives.apache.org/mod_mbox/commons-dev/201204.mbox/%3C20120418122114.GB32074%40dusk.harfang.homelinux.org%3E].
> It is now recognized that the values returned by {{guessParametersErrors()}}
> are in fact known as (asymptotic) standard errors. The javadoc should be made
> more explicit. Besides, the values returned by this method should be tested.
> The reference datasets from [NIST|http://www.itl.nist.gov/div898/strd/] are
> to be used.
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