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Question: Confidence intervals for parameters of NonlinearFit

Question:Confidence intervals for parameters of NonlinearFit

w-Teilchen 80 Maple
parameters interval
March 06 2015
2

Hej hej,

is there a way to obtain confidence intervals for the parameters in a NonlinearFit? To give you an impression of the problem which I was working on, I created a minimial working example (not sure wheather that actually helps). In this particular case, I have two parameters to fit the coefficients of a binomial series to some data I obtained. Beyond the values of the parameters (in a least square fit), I'm also interested in some kind of confidence interval, to get a feeling about how realiable my values are. Is there a direct (or even indirect) way to obtain such a thing. Either directly as a Maple function (confidenceintervals is not supported for NonlinearFit, if I'm not mistaken) or as something I can implement myself (within a reasonable time frame, as in hours rather than days).
Thanks in advance!

Cheer,

Sören

> 

restart; with(plots); with(Statistics)
> 

alpha[0] := 1.000000000:
> 

m__max := 4:
> 

model := Fit(pochhammer(z__1, m)*h__exp^m/factorial(m), [seq(m, m = 0 .. m__max)], [seq(alpha[m], m = 0 .. m__max)], m, output = [leastsquaresfunction, residuals], weights = [seq(1/abs(alpha[m]), m = 0 .. m__max)], iterationlimit = 10000)

model := [pochhammer(1.42349754368085, m)*16.2763580438677^m/factorial(m), Vector[row](5, {(1) = 0., (2) = -0.120508651249829e-1, (3) = 0.113910530162494e-1, (4) = 0.348907003220054e-3, (5) = -0.305508272150429e-2})]

 (1)
> 

plots[multiple](logplot, [{seq([m, alpha[m]], m = 0 .. m__max)}, style = point, color = black], [{seq([m, model[1]], m = 0 .. m__max)}])

 
> 

``

Download nonlinearfit-problem.mw
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