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Conditional moments for coordinates of stable vectors

Part of the Lecture Notes in Mathematics book series (LNM,volume 1391)

Abstract

An arbitrary symmetric α-stable (SαS) random vector has exactly the law of a normal random vector whose covariance is itself random and possesses the appropriate (α/2)-stable law (LePage, 1980). This fact is exploited in connection with the problem of prediction for SαS random vectors. The (α/2)-stable measure on covariances can be treated as an a-priori measure on nuisance parameters. It is found that the conditional expectation of one stable r.v. given another can (unexpectedly) be a.s. finite even for α≤1. This leads to predictors which take the form of a weighted average of predictors that would be used for the normal case. Such weighted averages are taken over the space of the covariances, according to an a-posteriori measure obtained by conditioning on the observations.

AMS 1980 Subject Classifications

  • Primary 60E07
  • Secondary 60G10

Research partially supported by the Office of Naval Research under grant USN N000014-85-K-0150 and Air Force Office of Scientific Research F49620 85 C 0144.

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References

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© 1989 Springer-Verlag

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LePage, R. (1989). Conditional moments for coordinates of stable vectors. In: Cambanis, S., Weron, A. (eds) Probability Theory on Vector Spaces IV. Lecture Notes in Mathematics, vol 1391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083388

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  • DOI: https://doi.org/10.1007/BFb0083388

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51548-7

  • Online ISBN: 978-3-540-48244-4

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