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A Nonparametric Sequential Test with Power 1 for the Mean of Lévy-stable Laws with Infinite Variance

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  • Abdelhakim Necir

    (Laboratory of Applied Mathematics)

Abstract

A nonparametric sequential test with power one for the mean of Lévy-stable laws with infinite variance is given. Our considerations are based on a law of the iterated logarithm for Peng’s estimator [Peng, Stat. Probab. Lett., 52:255–264, 2001] of the mean of heavy-tailed distributions. Our main motivation comes from applications to financial data, and in particular to sequential control of daily asset returns.

Suggested Citation

  • Abdelhakim Necir, 2006. "A Nonparametric Sequential Test with Power 1 for the Mean of Lévy-stable Laws with Infinite Variance," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 321-343, September.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:3:d:10.1007_s11009-006-9749-9
    DOI: 10.1007/s11009-006-9749-9
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    References listed on IDEAS

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    1. Rafał Weron, 2001. "Levy-Stable Distributions Revisited: Tail Index> 2does Not Exclude The Levy-Stable Regime," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 209-223.
    2. Einmahl, J. H. & Mason, D. M., 1988. "Strong limit theorems for weighted quantile processes," Other publications TiSEM 4bbe972d-b641-42a4-b2b8-0, Tilburg University, School of Economics and Management.
    3. Peng, Liang, 2001. "Estimating the mean of a heavy tailed distribution," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 255-264, April.
    4. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    5. Conti, Pier Luigi, 2005. "A nonparametric sequential test with power 1 for the ruin probability in some risk models," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 333-343, May.
    6. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    1. Djamel Meraghni & Abdelhakim Necir, 2007. "Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 557-572, December.

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