[SciPy-User] robust fit

[Charles R Harris]

On Tue, May 31, 2011 at 9:39 AM, <josef.pktd at gmail.com> wrote:

> On Tue, May 31, 2011 at 10:21 AM, Sturla Molden <sturla at molden.no> wrote:
> > Den 31.05.2011 16:10, skrev Sturla Molden:
> >> you want the minimize the sum of squares of weighted
> >> errors:
> >>
> >>      werror(x) = weight(error(x)) * error(x)
> >
> > One more thing: weight(error) is actually the square root of the
> > robust weighting function, as we want to minimize the sum of
> >
> >    robust_weight(error)  * (error**2)
>
> Do you have a reference or a full example for this?
>
> Your description sounds relatively simple, and I guess now that we
> (statsmodels) can get the non-linear version with only small(ish)
> changes and a call to a WNLLS (curve_fit) instead of WLS (linear).
>
>
I've also had good results with Tukey's biweight. As Sturla says, it can be
implemented as iterated weighted least squares. There is a whole class of
robust methods along that line. The L_1 cost function can also be done that
way, and the usual algorithm for the geometric median is one useful
application.

Chuck
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