[R] Huber location estimate

[Murray Jorgensen]

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
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