[R] Robust smoothing

[Martin Maechler]

  [Cross-posted to R-SIG-robust,
   the Special Interest Group (mailing list) on "Robustness and R"]

>>>>> "BertG" == Berton Gunter <gunter.berton at gene.com>
>>>>>     on Mon, 28 Nov 2005 11:42:45 -0800 writes:

    BertG> Note: As I believe Brian Ripley pointed out in his
    BertG> MASS book, loess may not be as resistant to outliers
    BertG> (which is one aspect of robustness; robustness of
    BertG> efficiency is another) as you think. The problem is
    BertG> that it starts off with LS estimates and these can be
    BertG> so distorted by unusual values that the reweighting
    BertG> cannot properly recover; i.e. convergence is to a
    BertG> local minimum far from the desired global one. 

indeed  {I've researched on that about 15 years ago as part of
my Ph.D.}.
I'm convinced that robust smoothing should be done quite
analogously to how (many agree) it should happen for parametric
regression:

1) initialized by a ``high breakdown'' (that's not a trivial notion when you do
   non-parametric curve estimation!) smoother;  
2) From that compute residuals r_i  and compute  weights w_i := psi(r_i)/r_i
   typically for a redescending psi.
3) Now use these weights for the ``high efficiency'' smoother,
   e.g., smooth.spline(), 
   maybe even without iterating {``1-step M-estimator'' idea}
   or then with iterating, i.e. reweighting.

For that reason, i.e. for being able to do "1)", 
I had collected algorithms for fast running medians {quite some time ago}
and added the R function  runmed()  {running medians}
which should be very fast, particularly for large data where
it's of optimal complexity see  help(runmed).

Martin Maechler, ETH Zurich


    BertG> You might wish to read the documentation for rlm() (in
    BertG> MASS, the package) and the appropriate sections of
    BertG> MASS, the book.

    BertG> Cheers,

    BertG> -- Bert Gunter Genentech Non-Clinical Statistics
    BertG> South San Francisco, CA
 
    BertG> "The business of the statistician is to catalyze the
    BertG> scientific learning process."  - George E. P. Box
 
 

    >> -----Original Message----- From:
    >> r-help-bounces at stat.math.ethz.ch
    >> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of
    >> Marta Colombo Sent: Monday, November 28, 2005 10:38 AM
    >> To: R help Subject: [R] Robust fitting
    >> 
    >> Good evening,I am Marta Colombo, student of "Politecnico
    >> di Milano". I'm studying Local Regression Techniques such
    >> as loess, smoothing splines and kernel
    >> smoothers. Choosing "symmetric" for the argument "family"
    >> in loess function it is possible to produce a robust
    >> estimate , in function smooth.spline and ksmooth I didn't
    >> find this possibility.  Well, is there a way to produce a
    >> robust estimate using smoothing splines or kernel
    >> smoothers? And if the answer is no, why? I'm asking these
    >> questions because I need to know loess' advantages and
    >> disadvantages compared to other techniques. Thank you
    >> very much for attention,
    >> 
    >> Marta Colombo