[R] p-values for robust regression

Martin Maechler maechler at stat.math.ethz.ch
Wed Jul 5 14:51:02 CEST 2006

  [Oops! Written 6 hours ago, the following was accidentally not sent.]

>>>>> "Celso" == Celso Barros <celso.barros at gmail.com>
>>>>>     on Wed, 5 Jul 2006 04:09:17 -0300 writes:

    Celso> When I run rlm to obtain robust standard errors, my output does not include
    Celso> p-values. Is there any reason p-values should not be used in this case? 

yes (see also below).

    Celso> Is there an argument I could use in rlm so that the output does
    Celso> include p-values?

What are the reasons?

How to properly do hypothesis testing in the context of robust
regression has partly been an open research problem.  Whereas
or has been solved in Elvezio Ronchetti's PhD thesis (1982)
by tau-tests, see chapter 7 of  Hampel, Rousseeuw, Ronchetti,
Stahel (1986), these are not (directly) related to standard
errors, and t-tests with some degrees of freedom.
Hence they are not so intuitively explainable, and not entirely
trivial to implement.  Probably this is one of reasons, why they
(tau-tests) haven't been programmed for MASS (the book and the R package).

Recent research, namely,
     Croux, C., Dhaene, G. and Hoorelbeke, D. (2003) _Robust standard
     errors for robust estimators_, Discussion Papers Series 03.16,
     K.U. Leuven, CES.
has been made use of by Matias Salibian-Barrera's roblm()
function now available as  lmrob() from package 'robustbase'.
There,  mod <- lmrob(........);  summary( mod ) 
does provide you with P-values.
But we still recommend *not* to ``believe in the P-values''
blindly, but rather base your data analysis on serious analysis
of residuals and other model checking.

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