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Exact Estimates for Moments of Random Bilinear Forms

Author

Listed:
  • R. Ibragimov

    (Yale University)

  • Sh. Sharakhmetov

    (Tashkent State Economics University)

  • A. Cecen

    (Central Michigan University)

Abstract

The present paper concentrates on the analogues of Rosenthal's inequalities for ordinary and decoupled bilinear forms in symmetric random variables. More specifically, we prove the exact moment inequalities for these objects in terms of moments of their individual components. As a corollary of these results we obtain the explicit expressions for the best constant in the analogues of Rosenthal's inequality for ordinary and decoupled bilinear forms in identically distributed symmetric random variables in the case of the fixed number of random variables.

Suggested Citation

  • R. Ibragimov & Sh. Sharakhmetov & A. Cecen, 2001. "Exact Estimates for Moments of Random Bilinear Forms," Journal of Theoretical Probability, Springer, vol. 14(1), pages 21-37, January.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:1:d:10.1023_a:1007812829787
    DOI: 10.1023/A:1007812829787
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    References listed on IDEAS

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    1. R. Ibragimov & Sh. Sharakhmetov, 1999. "Analogues of Khintchine, Marcinkiewicz–Zygmund and Rosenthal Inequalities for Symmetric Statistics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 621-633, December.
    2. Aydin Cecen, A. & Erkal, Cahit, 1996. "Distinguishing between stochastic and deterministic behavior in foreign exchange rate returns: Further evidence," Economics Letters, Elsevier, vol. 51(3), pages 323-329, June.
    3. Cecen, A. Aydin & Erkal, Cahit, 1996. "Distinguishing between stochastic and deterministic behavior in high frequency foreign exchange rate returns: Can non-linear dynamics help forecasting?," International Journal of Forecasting, Elsevier, vol. 12(4), pages 465-473, December.
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