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Limit points of sequences of moving maxima

Author

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  • Hebbar, H. V.
  • Vadiraja, N.

Abstract

Let Xn, n [greater-or-equal, slanted] 1 n0 [not double vertical, dash]e a sequence of independent random variables (r.v.'s) with the common distribution function (d.f.) F. Define the moving maxima Yk(n) = max(Xn - k(n) + 1, Xn - k(n) + 2,..., Xn) where k(n) is a sequence of positive integers. Under certain conditions on F and k(n), the set of all almost sure limit points of sequences of properly normalised Yk(n) is obtained.

Suggested Citation

  • Hebbar, H. V. & Vadiraja, N., 1997. "Limit points of sequences of moving maxima," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 13-18, May.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:1:p:13-18
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    References listed on IDEAS

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    1. Rothmann, Mark. D. & Russo, Ralph P., 1991. "Strong limiting bounds for a sequence of moving maxima," Statistics & Probability Letters, Elsevier, vol. 11(5), pages 403-410, May.
    2. Gut, Allan, 1990. "Limit points of sample maxima," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 331-336, April.
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    Cited by:

    1. Nayak, S. S. & Zalki, Madhusudhan, 2000. "On the fluctuations of independent copies of moving maxima," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 351-356, December.

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    1. Nayak, S. S. & Zalki, Madhusudhan, 2000. "On the fluctuations of independent copies of moving maxima," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 351-356, December.
    2. Rothmann, Mark D., 1997. "Stability of maxima over randomly deleted sets," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 145-152, December.

    More about this item

    Keywords

    Almost sure limit set Moving maxima;

    Statistics

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