I use NonlinearModelFit with additional constraints on the fitting parameteres. When I use "ParameterErrors" or "ParameterTable" mathematica throws the warning

FittedModel::constr: The property values {ParameterErrors} assume an unconstrained model. The results for these properties may not be valid, particularly if the fitted parameters are near a constraint boundary. >>.

When can I trust the estimated errors? What does "near" mean? Let's say I constrained my parameter to be bigger than zero and fitting gives a value of 0.026. Is that "near"? Is there some other really easy way to estimate the integrity of the fit. I noticed for example that the estimated error of the parameters is almost double the value of the estimated parameter. Not sure how to handle that. Does that mean the fit is bad (maybe a really dumb question, not sure)?

  • 1
    $\begingroup$ The sky is not falling. Mathematica is just acknowledging that its programmers understand the in's and out's of maximum likelihood estimation. So, first, I'd argue that this isn't a software issue with Mathematica and that the Cross Validated and/or Mathematics Stack Exchange sites would be better places to obtain an explanation of the issue. Very loosely the asymptotic estimators of the standard errors of the maximum likelihood estimators aren't very useful near the boundaries and don't exist at the boundaries. The mle parameter estimates are fine; just a problem with standard errors. $\endgroup$
    – JimB
    Apr 21, 2016 at 15:12
  • $\begingroup$ And to clarify my statement "The mle parameter estimates are fine" really means that they are "correct" in that they are the values that maximize the likelihood. I do not mean that they necessarily are close to the true values or that they have desirable properties for a finite sample. Your mileage may vary. $\endgroup$
    – JimB
    Apr 21, 2016 at 16:11
  • 2
    $\begingroup$ I'm voting to close this question as off-topic because the issue it raises is not a Mathematica issue but a mathematical one. That it is formulated in terms of Mathematica is not sufficient to make it an appropriate question for Mathematica.SE. $\endgroup$
    – m_goldberg
    Jun 27, 2016 at 1:10


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