[SciPy-User] Bootstrapping confidence interval of the maximum of a smoothing spline

[josef.pktd at gmail.com]

On Mon, Aug 22, 2011 at 5:48 PM, Giovanni Luca Ciampaglia
<ciampagg at usi.ch> wrote:
> Hi all, I have data on editing activity from an online community and I am
> trying to estimate the day of peak activity using smoothing splines.
>
> I determine the smoothing factor for scipy.interpolate.UnivariateSpline by
> leave-1-out crossvalidation, and then use scipy.optimize.fmin_tnc to
> evaluate the maximum from the resulting spline. This works pretty well and
> seems robust enough (e.g. http://tinypic.com/r/a3m739/7). Now I would like
> to compute the confidence intervals for this estimate, but I am not exactly
> sure on how to proceed, since I cannot sample data from my non-parametric
> model and generate a distribution for this estimator.

My first idea would be to sample the residuals, the deviation from the
actual observations and the spline, add them to the spline, and
estimate the new spline on the generated data. And repeat for a number
of bootstrap samples.

Josef

>
> I was thinking at applying some noise to the smoothing factor, but I am not
> sure whether this approach has any theoretical basis. Any idea?
>
> Cheers,
>
> --
> Giovanni Luca Ciampaglia
>
> Ph.D. Candidate
> Faculty of Informatics
> University of Lugano
> Web: http://www.inf.usi.ch/phd/ciampaglia/
>
> Bertastraße 36 * 8003 Zürich * Switzerland
>
>
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