This is a difficult task.  If Xand Yare bivariate normal then the regression
E[Y|X] is linear.  If they are bivariate alpha stable the regression is non
linear. Have a look at the material on multivariate alph stable
distributions in Uchaikin and Zolotarev (1999), Chance and Stability, VSP.
There are details of the estimation in Canbanis, Samorodnitsky and Taqqu
(1991), Stable Processes and Related Processes, Birkhauser.

In
http://www.tcd.ie/Economics/staff/frainj/Stable_Distribution/thesis_main_5.pdf.
There is a chapter dealing with the case where the regressors are fixed and
the residual is alpha stable.  In that case I did not use R as I had
considerable problems with fitting the required alpha stable functions in R.

You might also look at John P Nolan's alpha stable libraries.  There is a
version available for R which extends the alpha stable facilities available
in R.

Best Regards

John

On Sunday, 14 August 2011, Pascal Grosbuis <pascal.grosbuis@orange.fr>
wrote:
> Hello !
>
> I'm already using "fBasics" to generate alpha-stable variables or compute
their density or distribution function but
> do you know where I could find .R tools for computing the correlation and
fit a regression between two
> alpha-stable variables ?
>
> Thanks in advance !
>
> Kind regards,
>
> Pascal Grosbuis
> (France)
>        [[alternative HTML version deleted]]
>
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>

-- 
John C Frain
Economics Department
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.html
mailto:frainj@tcd.ie
mailto:frainj@gmail.com

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