On the Conditional Variance-Covariance of Stable Random Vectors, II

  • Stergios B. Fotopoulos
Part of the Trends in Mathematics book series (TM)


Under the assumption that X = (X 1, X 2) a (n 1 + n 2)-dimensional vector is strictly α-stable distributed, the conditional variance-covariance of X 2 given X 1 is expressed in terms of the spectral measure T. Moreover, if some additional assumptions on the vector X 1 are imposed such that the coordinates are statistically independent, then an additive expression for the conditional variance-covariance is found. A trigonometric unified method is presented for establishing these expressions.

Key words and phrases

Stable distributions conditional moments nonlinear regression 


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  1. Cambanis, S. and Fotopoulos, S. (1995). Conditional variance for stable random vectors. Probab. Math. Statist., 15, 195–214.MathSciNetzbMATHGoogle Scholar
  2. Cambanis S., Fotopoulos S., and He, L. (1997). On the conditional variance for scale mixtures of normal distributions. Technical Report, Washington State University.Google Scholar
  3. Cambanis, S. and Wu, W. (1992). Multiple regression on stable vectors. J. Multivariate Anal. 41, 243–272.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Cioczek-Georges R. and Taqqu M. (1993). Form of the Conditional Variance for Stable Random Variables. Technical Report, Boston University.Google Scholar
  5. Hardin, C, Samorodnitsky, G. and Taqqu, M. (1991) Nonlinear progression of stable random variables. Ann. Appl. Prob. 1,582–612.MathSciNetzbMATHCrossRefGoogle Scholar
  6. Kolmogorov, A.N., and Fomin, S.V.(1970). Introductory Real Analysis. Dover Publ., Inc.Google Scholar
  7. Samorodnitsky, G and Taqqu, M.S. (1991) Conditional moments and linear regression for stable random variables. Stochast. Proc. Applic, 39, 183–199.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Wu, W. and Cambanis, S. (1991). Conditional Variance of Symmetric Stable Variables. In G. Samorodnitsky, S. Cambanis, and M. S. Taqqu, Editors, Stable and Related Topics, 25, Progress in Probability, 85–99, Birkhäuser Boston.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Stergios B. Fotopoulos
    • 1
  1. 1.Department of Management and Systems and Program in StatisticsWashington State UniversityPullmanUSA

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