partially linear models

From: Peter Dalgaard

"Liaw, Andy" <andy_liaw at merck.com> writes:

This doesn't look like an R question, as I know of no pre-packaged
functionality publicly available that can fit the model 

that Elizabeth

described, and it doesn't seem like she's particularly 

interested in an

R-based answer, either.

My gut feeling is that if there is a test of significance 

for beta in such a

model, it probably shouldn't depend upon how f() is fitted, 

wavelets or

otherwise.  I.e., any test for the linear component in a 

partially linear

model ought to do just fine.  The main difference here, 

from a fully linear

model, is that one no longer can estimate E(y) without 

bias, even with the

assumption that the model is correct.  What gets messier still is if
data-dependent smoothing/de-noising is done in estimating 

f(), as that opens

up a whole bucket of nasty creatures.

I could be off, though, so take this with a truck-load of NaCl...

Isn't it just a gam() model (package mgcv), if you replace the
wavelets with splines?

I believe so.
 

I haven't messed with this for a decade, but I seem to recall that
there's a result to the effect that you need to undersmooth f slightly
to get optimal inference for the beta. Perhaps look in Green &
Silverman for the reference. 

A quote I heard from Prof. David Ruppert:  "There are lies, damned lies, and
then big O notations."

I presume the need to undersmooth is to reduce the bias of the `smooth'.
The problem is, by how much should one undersmooth, so the bias would go
from O(k*n^-4) to O(k*n^-5) (I'm just making this up, but you get the idea)?

Cheers,
Andy

Andy

From: Spencer Graves

	  I have seen no replies to this post, and I don't know 
that I can 
help, either.  However, I wonder if you tried 

"RSiteSearch" with your 

favorite key words and phrases?  For example, I just got 

107 hits for 

'RSiteSearch("wavelets")'.  I wonder if any of them might 

help you.

	  If you'd like further help from this list, please 
submit another 
post.  However, before you do, I suggest you read the 

posting guide! 

"www.R-project.org/posting-guide.html".  Anecdotal 

evidence suggests 

that posts more consistent with the guide tend to receive 
quicker, more 
useful replies.

	  Best Wishes,
	  spencer graves

Elizabeth Lawson wrote:

Hey,
   
   I am estiamting a partially linear model 

y=X\beta+f(\theta) where the f(\theta) is estiamted using 

wavelets.

   
  Has anyone heard of methods to test if the betas are 

significant or to address model fit?

   
  Thanks for any thoughts or comments.
   
  Elizabeth Lawson

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