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physicist
09-10-2007, 12:16 PM
Sirs,

Given their strong tradition in both numerical analysis and
statistics: Is IMSL considering to add L^p norm regression
to their palette? (with k=1,2,3, ... regression variables)

A separate algorithm may be needed for p=1 and 1<p<2.

This is a robust form of regression, resistant against outliers.
(It is the symmetric form of quantile regression, used in R, and
developed by Koenker.) p=1 ('turtle') stems from Laplace,
p=2 ('Achilles') from Gauss.

A few references (perhaps not the most recent ones) are:

A. Ronner, p-norm estimators in a linear regression model, PhD Thesis,
Groningen University (1977) - basic theory.

K. Knight, Limiting distributions for L1 regression estimators, The Annals of Statistics, 26 (1998) 755-770.

V.A. Sposito et al., Algorithm AS 110, Applied Statistics 26 (1977) 114-118.
- univariate regression only.

Yours faithfully,

physicist.

ed
09-11-2007, 05:12 AM
I can certainly file an Enhancement Request for you. Can you have a look at lnorm_regression (http://www.vni.com/products/imsl/documentation/CNL06/stat/NetHelp/default.htm?turl=lnormregression.htm) and confirm that this isn't quite what you're looking for?

Richard Hanson
09-11-2007, 07:29 AM
If your problem is a linear, over-determined system, take a look at the IMSL FNL Statistics Library, Chapter 2, routines RLAV and RLLP. See if these come close to what you have in mind.

physicist
09-11-2007, 07:58 AM
Thank you for your reply. However, the problem is not a linear one for 1 < p < 2.

physicist
09-11-2007, 08:06 AM
I can certainly file an Enhancement Request for you. Can you have a look at lnorm_regression (http://www.vni.com/products/imsl/documentation/CNL06/stat/NetHelp/default.htm?turl=lnormregression.htm) and confirm that this isn't quite what you're looking for?

That is precisely what I was looking for! :) The only remaining question is, perhaps, whether it is, or will be, included in the FORTRAN-90/95 version.

ed
09-11-2007, 10:33 AM
That is precisely what I was looking for! :) The only remaining question is, perhaps, whether it is, or will be, included in the FORTRAN-90/95 version.

lnorm_regression actually appears in the IMSL Fortran library as RLAV (http://www.vni.com/products/imsl/documentation/fort06/stat/NetHelp/default.htm?turl=rlav.htm), RLLP (http://www.vni.com/products/imsl/documentation/fort06/stat/NetHelp/default.htm?turl=rllp.htm), and RLMV (http://www.vni.com/products/imsl/documentation/fort06/stat/NetHelp/default.htm?turl=rlmv.htm) - the codes that Dr. Hanson mentioned above. I'm not sure if these will fit for your nonlinear case, but check them out and let us know.

Richard Hanson
09-11-2007, 11:02 AM
You can assist by giving an example of a non-linear l^p regression problem that you need to solve. Also mention any constraints you need to include.

To start the discussion we will have m conditional equations, r_i(x)\approx 0,\ i=1,...,m. The objective is to compute x that minimizes\sum |r_i(x)|^p,\ 1<p<2. What are typical functions r_i(x)? What is the size of m ? Anything else special may be helpful.

If you wish, respond using the LaTex MUL mentioned under the "sticky" headings above.

Richard Hanson
09-13-2007, 07:05 AM
Your response was mailed and I think it best to take this off-line. Thank you for taking the trouble to reply.

physicist
09-13-2007, 09:44 AM
Thank you for your professional reply.

Since I have no doubt you will I agree reading the three suggestions critically,
and come back in case of disambiguity, I agree to take the topic off-line.

With best regards,

physicist

physicist
09-19-2007, 09:53 AM
Now then ... I have attached suggestion in its present form as 1page file,
knowing that implementation requires quite some effort.

With best regards,
physicist.