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Complete asymptotic expansions for normal extremes

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  • Nadarajah, Saralees

Abstract

Hall (1979) was the first to derive the rate of convergence for normal extremes. Many authors have followed up the work of Hall, but complete asymptotic expansions have not been known for normal extremes. Here, we derive such expansions for the first time. The expansions are single infinite sums of terms involving Bell polynomials and Stirling numbers. The usefulness of the expansions over the results in Hall is illustrated computationally.

Suggested Citation

  • Nadarajah, Saralees, 2015. "Complete asymptotic expansions for normal extremes," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 127-133.
    • Handle: RePEc:eee:stapro:v:103:y:2015:i:c:p:127-133
    DOI: 10.1016/j.spl.2015.04.026
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    References listed on IDEAS

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    1. Hashorva, Enkelejd, 2010. "Asymptotics of the norm of elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 926-935, April.
    2. Hashorva, Enkelejd, 2009. "Asymptotics for Kotz Type III elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 927-935, April.
    3. Dȩbicki, Krzysztof & Hashorva, Enkelejd & Ji, Lanpeng & Tabiś, Kamil, 2014. "On the probability of conjunctions of stationary Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 141-148.
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    Cited by:

    1. Nadarajah, Saralees, 2016. "Asymptotic expansions for bivariate normal extremes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 124-133.

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