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Petipace
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Joined: January 21st, 2019, 4:33 am

### Re: Smoothing splines (clamped spline)

You could take a look at http://www.netlib.org/dierckx/.

concur.f implements the clamped smoothing spline.

Disclaimer: I haven’t used this library myself, but Dierckx’s book is quite good.

Alan
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### Re: Smoothing splines (clamped spline)

You could take a look at http://www.netlib.org/dierckx/.

concur.f implements the clamped smoothing spline.

Disclaimer: I haven’t used this library myself, but Dierckx’s book is quite good.

Thank you -- it looks like Dierckx's book may indeed have what I am searching for -- ordered a decently priced used copy.

Cuchulainn
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### Re: Smoothing splines (clamped spline)

FaridMoussaoui
Posts: 412
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Location: Genève, Genf, Ginevra, Geneva

### Re: Smoothing splines (clamped spline)

That's package was removed from CRAN repos. Orphaned and archived on 2014.
It was mainly a call to the fortran librairies.

Cuchulainn
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### Re: Smoothing splines (clamped spline)

That's package was removed from CRAN repos. Orphaned and archived on 2014.
It was mainly a call to the fortran librairies.
All that work for nothing?

FaridMoussaoui
Posts: 412
Joined: June 20th, 2008, 10:05 am
Location: Genève, Genf, Ginevra, Geneva

### Re: Smoothing splines (clamped spline)

It means it is not actively maintained but it is still there. I even installed it for a test and it's working (you need a fortran compiler).

Cuchulainn
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### Re: Smoothing splines (clamped spline)

This might be useful; in particular, estimation of the smoothing parameter $\lambda$.

Cuchulainn
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### Re: Smoothing splines (clamped spline)

Hi Daniel,

Thank you for the code. I haven't opened it yet. Let me know if I will find the solution to the following problem, which will answer your question.

I want to find the piecewise cubic polynomial $g(t)$ that solves the following problem:

(*) minimize $\left( \sum_{i=1}^n \{ y_i - g(t_i) \}^2 + \lambda \int_a^b \{ g''(u) \}^2 \, du \right)$,

subject to
(A) given values for $g'(a)$ and $g'(b)$, where $a < t_1 < t_2 < \cdots < t_n < b$,
(B) given data $\{t_i,y_i\}$ and
(C) given $\lambda > 0$, the 'smoothing' parameter.

Without (A), this is the standard smoothing spline problem, solved by Reinsch (1967) (fulltext here) and with many subsequent treatments.

BTW, I've got your 2018 book. Correct me if I'm wrong, but it looks like the cubic splines discussed there are just *interpolating* splines; i.e., the solution to (*) when $\lambda=0$?
.
Alan,
Don't suppose you have a numeric example for this?