how to use the basis matrix of "ns" in R? really confused by multi-dim spline filtering?

Dear Micheal,

 > the output of the "ns" function in R is "basis matrix", but then
Yes you are right, the output of the ns(x, df) is the basis matrix of a 
natural cubic spline with df degrees of freedom. See ?ns (in package 
splines) on how to specify df or knots or ..

Fitting y~ns(x,df) yields a smooth curve given by a linear combination 
of the basis functions (the single colums of the basis matrix) by the 
estimated coefficients (returned by the fitted model).

As far as I know, a tensor product is usually employed to 
multidimensional smoothing and the multidimensional basis is formed via 
the kronecker product of the marginal bases.

Finally, last but not least: Probably you need some statistical 
backaground on spline fitting..
Please, read some statistical papers/books on such topic (for instance 
see references in packages splines, mgcv)

best,
vito

Hi all,

Could anybody recommend some easy-to-understand and example based
notes/tutorials on how to use cubic splines to do filtering on
multi-dimension data?

I am confused by the 1-dimensional case, and more confused by
multi-dimensional case.

I found all the books suddenly become very abstract when it comes to this
subject.

They don't provide examples in R or Splus at all.

Specifically, I don't know how to provide data "x" to the "ns" function in
R,

and I don't understand what should be the output matrix, and how to use the
output matrix to "filter" data?

Books mention about basis matrix, design matrix, model matrix, data matrix,
etc. I got lost.

I presume the output of the "ns" function in R is "basis matrix", but then
how do I use it?  How to form tensor-product?

I don't understand it at all.

Please help me!

Thank you very much!

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Vito M.R. Muggeo
Dip.to Sc Statist e Matem `Vianelli'
Universit?? di Palermo
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90128 Palermo - ITALY
tel: 091 6626240
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