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A strong invariance principle for the logarithmic average of sample maxima

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  • Fahrner, Ingo

Abstract

Given an extremal-[Lambda] process {Y[Lambda](t), t>0}, the transformed process {U(s)=Y[Lambda](es)-s, -[infinity]

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:93:y:2001:i:2:p:317-337
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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 & 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.
    3. Fahrner, Ingo, 2000. "An extension of the almost sure max-limit theorem," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 93-103, August.
    4. Gouet, Raúl, 1989. "Embedding in extremal processes and the asymptotic behavior of sums of minima," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 219-223, August.
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    Cited by:

    1. Stadtmüller, U., 2002. "Almost sure versions of distributional limit theorems for certain order statistics," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 413-426, July.
    2. 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.
    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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