Re: [R] Huber location estimate

From: Murray Jorgensen <maj_at_stats.waikato.ac.nz>
Date: Thu 22 Dec 2005 - 20:13:45 EST

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@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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Received on Thu Dec 22 20:19:36 2005

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