[SciPy-user] non-linear model coefficient standard error estimates

Robert Kern robert.kern at gmail.com
Thu Jan 25 14:35:16 CST 2007

zunzun at zunzun.com wrote:
> I can easily calculate coefficient standard errors for
> linear models such as this cubic polynomial:
> y = ax^0 + bx^1 + cx^2 + dx^3
> using the scipy Cookbook code referenced at
> http://scipy.org/Cookbook/OLS
> I do not know how to estimate coefficient standard errors
> for non-linear models such as
> y = exp(ax - b)
> Can anyone point me at a reference?  I'll add it to
> the Python Equations project as soon as I can.

scipy.odr gives error estimates for such nonlinear parameters. A description of
their method (which works for nonlinear OLS models) is given in this paper:

Paul T. Boggs and Janet E. Rogers (1990), ``The Computation and Use of the
Asymptotic Covariance Matrix for Measurement Error Models,'' NIST IR 89-4102,
U.S. Government Printing Office.

Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
 that is made terrible by our own mad attempt to interpret it as though it had
 an underlying truth."
  -- Umberto Eco

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