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nikol


Total Posts: 676
Joined: Jun 2005
 
Posted: 2019-02-19 21:58
I did this 100 times, but doing 101st started to ask myself...

Problem:
Suppose I fit a function with 5 parameters to 20 points. => dof = 20-5 = 15.
For this I construct R2 which in principle follows Chi2 (assuming errors are normal).
Fitting procedure is done iteratively, by removing or adding points to the fit, which means that dof is dynamic. For example, by removing 2 outliers, I will have dof = 13, But then R2(dof=15) is not the same as R2(dof=13).

It occurs to me that I have to minimise this (x) function:



but it is costly from calculation perspectives.
Is there something simpler? I looked into adaptive filtering, adaptive noise cancellation, but without any appeal.

PS. I confess, all my life, I minimised Chi2/dof. However, given that mean(Chi2) ~ dof and var(Chi2) ~ 2*dof I should do it differently.

PSS. As usual, answer comes after telling someone. I have to minimize this function:



or simply

Chi2/sqrt(2*dof)
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