[R] Huber location estimate
Murray Jorgensen
maj at stats.waikato.ac.nz
Thu Dec 22 10:13:45 CET 2005
Prof Brian Ripley wrote:
> On Thu, 22 Dec 2005, Murray Jorgensen wrote:
>
>> We have a choice when calculating the Huber location estimate:
>> > set.seed(221205)
>> > y <- 7 + 3*rt(30,1)
>
>
> That's Cauchy, BTW, a very extreme case.
Sure, the sort of situation where one might want a robust estimator.
[...]
> Note that the huber() scale estimate is the initial MAD, whereas rlm
> iterates. Because during iteration the 'center' for MAD is known to be
> zero, the results differ. For symmetric distributions there is little
> difference, but your sample is not close to symmetric.
[Blush] yes I knew that and somehow I forgot. But leave rlm() alone for
a while and do IRLS with fixed scale:
th <- median(y)
s <- mad(y)
# paste this in a few times:
w <- ifelse((y-th< 1.345*s & y-th>-1.345*s), 1, 1.345*s/abs(y-th))
th <- weighted.mean(y,w)
th
We converge to
> th
[1] 5.9203
close to the answer given by rlm() different from
> huber(y)$mu
[1] 5.9117
So the variable scale does not account for the difference.
Murray Jorgensen
--
Dr Murray Jorgensen http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz Fax 7 838 4155
Phone +64 7 838 4773 wk Home +64 7 825 0441 Mobile 021 1395 862
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