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# Non-linear regression of stable random variables

**Clyde D. Hardin Jr.
**

Gennady Samorodnitsky

Murad S. Taqqu

### Abstract:

*Let be an -stable random vector, not necessarily symmetric,
with . The paper investigates the regression for all values of . We give conditions for the existence of the
conditional moment
when , and we obtain an
explicit form of the regression as a function of ***x**. Although
this regression is, in general, not linear, it can be linear even when the
vector
is skewed. We give a necessary and sufficient condition for
linearity and characterize the asymptotic behavior of the regression as
. The behavior of the regression functions is also
illustrated graphically.