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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.