Hello Stefan,
The summary() method for lmRob objects in package robust returns
estimated standard errors that are valid when the error distribution is
symmetric. If you either (a) don't have outliers in your data; or (b)
have atypical observations or model departures that are symmetric around
the regression line, then these estimated SDs could be used to construct
confidence intervals for each regression coefficient of the form
estimate +/- qnorm(alpha/2) * SD.
However, in package robustbase, the summary() method for lmrob objects
returns estimated SDs that are valid in more general cases (e.g
asymmetric outliers), so they are in principle more reliable than the
ones above. They are based on Croux, C., Dhaene, G., Hoorelbeke, D.
(2003), "Robust Standard Errors for Robust Estimators." (available on
line from Christophe Croux's website). See help(lmrob) for more details.
These estimated SDs in package robustbase can also be used to construct
confidence intervals for each regression coefficient of the form
estimate +/- qnorm(alpha/2) * SD under weaker (more general) assumptions
than above.
Moreover, note that bootstrapping robust estimators is not
straightforward. Although MM estimators are smooth enough to allow the
bootstrap to be consistent, their high computational complexity together
with the potentially large number of outliers present in the bootstrap
samples makes direct bootstrapping of robust estimators not a good idea
in general. There are some alternatives in the literature. See, for
example: SB and Zamar, R.H. (2002). Bootstrapping robust estimates of
regression. The Annals of Statistics, 30, 556-582.
This fast and robust bootstrap can also be applied to obtain consistent
p-values for nested tests of hypotheses for linear regression models
based on robust estimators (SB, (2005). Estimating the p-values of
robust tests for the linear model. Journal of Statistical Planning and
Inference, 128, 241-257).
The fast and robust bootstrap has also been applied successfully to
several other models (e.g. SB, Van Aelst, S. and Willems, G. (2006). PCA
based on multivariate MM-estimators with fast and robust bootstrap.
Journal of the American Statistical Association, 101, 1198-1211;
Roelant, E., Van Aelst, S., and Croux, C. (2008), " Multivariate
Generalized S-estimators," Journal of Multivariate Analysis, to appear;
Van Aelst, S., and Willems, G. (2005), " Multivariate Regression
S-Estimators for Robust Estimation and Inference," Statistica Sinica,
15, 981-1001), and also to model selection for linear regression (SB,
Van Aelst, S. (2008), " Robust Model Selection Using Fast and Robust
Bootstrap, " Computational Statistics and Data Analysis, 52, 5121-5135).
I have some R plug-in code for the robustbase package that implements
this fast and robust bootstrap based on lmrob in package robustbase. If
you're interested, let me know and I will dig it out for you.
Hope this helps. I'll be happy to help if you have any further questions.
Best,
Matias
--
_____________________________________________________
Matias Salibian-Barrera - Department of Statistics
The University of British Columbia
Phone: (604) 822-3410 - Fax: (604) 822-6960
"The plural of anecdote is not data" (George Stigler?)
Stefan Herzog wrote:
Hi,
I looked around, but couldn't find anything (and that's why I hope this
is not an unnecessary, lazy newbie question):
1) How do I compute confidence intervals for lmRob regression (package
"robust")?
2) If this method is not yet implemented, would it make sense to
bootstrap lmRob and derive the CI, say using a percentile t method?
Thanx!
Cheers, Stefan
-------------------------------------------------------------
Stefan Herzog, M. Sc.
Center for Cognitive and Decision Sciences
Department of Psychology
University of Basel
Missionsstrasse 64A
4055 Basel
Switzerland
+41 61 267 06 15
[EMAIL PROTECTED]
http://www.psycho.unibas.ch/herzog/
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