Nonlinear regression of stable random variables
Hardin, Clyde D., Jr
Taqqu, Murad S.
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Citation (published version)Clyde D Hardin Jr, Gennady Samorodnitsky, Murad S Taqqu. 1991. "Nonlinear Regression of Stable Random Variables." The Annals of Applied Probability, Volume 1, no. 4. pp. 582 - 612. https://doi.org/10.1214/aoap/1177005840
Let (X1,X2) be an α-stable random vector, not necessarily symmetric, with 0<α<2. This article investigates the regression E(X2∣X1=x) for all values of α. We give conditions for the existence of the conditional moment E(|X2|p|X1=x) when p≥α, and we obtain an explicit form of the regression E(X2∣X1=x) as a function of x. Although this regression is, in general, not linear, it can be linear even when the vector (X1,X2) is skewed. We give a necessary and sufficient condition for linearity and characterize the asymptotic behavior of the regression as x→±∞. The behavior of the regression functions is also illustrated graphically.
Rights© 1991 Institute of Mathematical Statistics