Re: Fitting step function
- To: mathgroup at smc.vnet.net
- Subject: [mg122206] Re: Fitting step function
- From: premiumxy <spam at stefanabel.com>
- Date: Fri, 21 Oct 2011 06:21:33 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
For some reasons I could not find Barrie's reply to my message on the discussion forum. I am posting it here:
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Hi premiumxy
Attached is my full Notebook for your question (typical of those that I construct anytime I look at a question on MathGroup).
It appears from the failures for HeavisideTheta[.] and UnitStep[.] in Sections 3 and 4 respectively that there is no explicit and differentiable "time of jump" parameter in the definitions or internal representations of either these two functions.
Hence the infinite confidence intervals, and the fact that the returned least-squares value for "t" (the moment of the phase change) is just the given starting value.
My ArcTan function does have such a parameter, hence the sensible least-squares value and associated confidence interval.
For your actual data, as you can see I get {-0.0474718, {-0.729055, 0.634111}} for the point estimate and 95%CI for the moment of the phase change neasr zero. I don't know how you would get anything for around -70, as you suggest. There doesn't seem to be a jump there ...
I hope this helps.
Cheers
Barrie
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