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Does asymptotic linearity of the regression extend to stable domains of attraction?

Renata Cioczek-Georges
Murad S. Taqqu

Abstract:

Hardin, Samorodnitsky, Taqqu (1991) have shown that the regression is typically asymptotically linear when is an -stable random vector with . We provide necessary and sufficient conditions for asymptotic linearity of where is an -stable random vector and is a random variable, independent of , such that is in the domain of normal attraction of X. Asymptotic linearity does not always hold even when is linear. For some distributions of , the asymptotic rate of fluctuates.