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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© 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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