Confidence intervals estimates for cubic smoothing spline (csaps)

Question

Matthew Taliaferro 2017-5-23

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回答： Matthew Taliaferro 2017-5-29

Is there a built in function that will return the confidence bands for csaps (or the output from ppval)? Extra information that might be useful:

I have data that is smoothed both with and without weights.
I estimated the smoothing parameter using cross-validation using both k-fold and leave-one-out. Aside: why doesn't MATLAB do this automatically?

I found a paper, Smoothing Noisy Data with Spline Functions by M. F. Hutchinson and F. R. De Hoog that describes a method for estimating the confidence intervals, but I'd rather not code it myself if a script already exists.

Edit: The title was poorly worded and it doesn't seem I can change it now. I meant confidence bands, not confidence interval.

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Answer 1

Matthew Taliaferro 2017-5-29

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I wrote my own code and posted it here. Hopefully it's useful for someone.

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Answer 2

David Ding 2017-5-26

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Hi Mark,

Unfortunately the output of "csaps" function requires further processing to obtain the confidence bands. The following detailed explanations on the Curving Fitting Toolbox might be useful:

https://www.mathworks.com/help/curvefit/confidence-and-prediction-bounds.html

Thanks,

David

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Matthew Taliaferro 2017-5-26

Thank you for taking the time to answer my question. The doc page for confint() and predint() both say you cannot use them for calculating confidence or prediction intervals for non-parametric regression models. I wish it had been that easy :(

Again, thanks for the help.

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