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A note on maxima of bivariate random vectors

Author

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  • Hooghiemstra, G.
  • Hüsler, J.

Abstract

For i.i.d. bivariate normal vectors we consider the maxima of the projections with respect to two arbitrary directions. A limit theorem for these maxima is proved for the case that the angle of the two directions approaches zero. The result is generalized to a functional limit theorem.

Suggested Citation

  • Hooghiemstra, G. & Hüsler, J., 1996. "A note on maxima of bivariate random vectors," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 1-6, December.
    • Handle: RePEc:eee:stapro:v:31:y:1996:i:1:p:1-6
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    References listed on IDEAS

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    1. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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    Cited by:

    1. Kabluchko, Zakhar, 2009. "Extremes of space-time Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3962-3980, November.
    2. Tang, Linjun & Zheng, Shengchao & Tan, Zhongquan, 2021. "Limit theorem on the pointwise maxima of minimum of vector-valued Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 176(C).
    3. Enkelejd Hashorva & Zuoxiang Peng & Zhichao Weng, 2016. "Higher-order expansions of distributions of maxima in a Hüsler-Reiss model," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 181-196, March.

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