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The logarithmic average of sample extremes is asymptotically normal

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  • Berkes, István
  • Horváth, Lajos

Abstract

We obtain a strong approximation for the logarithmic average of sample extremes. The central limit theorem and laws of the iterated logarithm are immediate consequences.

Suggested Citation

  • Berkes, István & Horváth, Lajos, 2001. "The logarithmic average of sample extremes is asymptotically normal," Stochastic Processes and their Applications, Elsevier, vol. 91(1), pages 77-98, January.
    • Handle: RePEc:eee:spapps:v:91:y:2001:i:1:p:77-98
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    References listed on IDEAS

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    1. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
    2. Berkes, István & Csáki, Endre & Horváth, Lajos, 1998. "Almost sure central limit theorems under minimal conditions," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 67-76, January.
    3. Ibragimov, Ildar & Lifshits, Mikhail, 1998. "On the convergence of generalized moments in almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 343-351, November.
    4. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    5. Berkes, István & Horváth, Lajos & Khoshnevisan, Davar, 1998. "Logarithmic averages of stable random variables are asymptotically normal," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 35-51, September.
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    Cited by:

    1. Csáki, Endre & Gonchigdanzan, Khurelbaatar, 2002. "Almost sure limit theorems for the maximum of stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 195-203, June.
    2. Fahrner, Ingo, 2001. "A strong invariance principle for the logarithmic average of sample maxima," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 317-337, June.
    3. Berkes, István & Weber, Michel, 2006. "Almost sure versions of the Darling-Erdös theorem," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 280-290, February.

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