[R] prediction intervals for robust regression

[Prof Brian Ripley]

On 11/02/2015 19:38, Bert Gunter wrote:
> Presumably you've checked out:
>
> http://cran.r-project.org/web/views/Robust.html
>
> If you can estimate the variance of parameter estimates, betahat, then
> you can estimate the variance of a predicted value, X betahat; add the
> estimated variance of individuals to this if that's what you're
> looking for (and it's not already available).

But that's not too much use without some idea of the error distribution, 
and using robust statistics assumes it is non-normal, long-tailed.  And 
it is unusual to have enough data to estimate the tail behaviour of such 
a distribution.

It might be better to do this with a parametric model with a long-tailed 
error distribution, especially if there is evidence (e.g. from other 
samples) about the latter.

> Further questions should go to a statistics site like
> stats.stackexchange.com, as statistical questions are off topic here.

Agreed.


>
> Cheers,
> Bert
>
> Bert Gunter
> Genentech Nonclinical Biostatistics
> (650) 467-7374
>
> "Data is not information. Information is not knowledge. And knowledge
> is certainly not wisdom."
> Clifford Stoll
>
>
>
>
> On Wed, Feb 11, 2015 at 11:03 AM, Burns, Jonathan (NONUS)
> <Jonathan.Burns1 at gdit.com> wrote:
>> I have created robust regression models using least trimmed squares and MM-regression (using the R package robustbase).
>>
>> I am now looking to create prediction intervals for the predicted results.  While I have seen some discussion in the literature about confidence intervals on the estimates for robust regression, I haven't had much success in finding out how to create prediction intervals for the results.  I was wondering if anyone would be able to provide some direction on how to create these prediction intervals in the robust regression setting.
>>
>> Thanks,
>>
>> Jonathan Burns
>> Sr. Statistician
>> General Dynamics Information Technology
>> Medicare & Medicaid Solutions
>> One West Pennsylvania Avenue
>> Baltimore, MD 21204
>> (410)-842-1594
>> Jonathan.Burns1 at gdit.com<mailto:Jonathan.Burns1 at gdit.com>
>> www.gdit.com<http://www.gdit.com/>


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Emeritus Professor of Applied Statistics, University of Oxford
1 South Parks Road, Oxford OX1 3TG, UK