[R] linear functional relationships with heteroscedastic & non-Gaussian errors - any packages around?

Jarle Brinchmann jbrinchmann at gmail.com
Tue Dec 2 19:58:40 CET 2008

Thanks for the reply!

On Tue, Dec 2, 2008 at 6:34 PM, Prof Brian Ripley <ripley at stats.ox.ac.uk> wrote:
> I wonder if you are using this term in its correct technical sense.
> A linear functional relationship is
> V = a + bU
> X = U + e
> Y = V + f
> e and f are random errors (often but not necessarily independent) with
> distributions possibly depending on U and V respectively.

This is indeed what I mean, poor phrasing of me. What I have is the
effectively the PDF for e & f for each instance, and I wish to get a &
b. For Gaussian errors there are certainly various ways to approach it
and the maximum-likelihood estimator is fine and is what I normally
use when my errors are sort-of-normal.

However in this instance my uncertainty estimates are strongly
non-Gaussian and even defining the mode of the distribution becomes
rather iffy so  I really prefer to sample the likelihoods properly.
Using the maximum-likelihood estimator naively in this case is not
terribly useful and I have no idea what the derived confidence limits

Ah well, I guess what I have to do at the moment is to use brute force
and try to calculate P(a,b|X,Y) properly using a marginalisation over
U (I hadn't done that before, I expect that was part of my problem).
Hopefully that will give reasonable uncertainty estimates, lots of
pain for a figure nobody will look at for much time :)


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