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A fast algorithm to sample the number of vertexes and the area of the random convex hull on the unit square

Author

Listed:
  • Chi Ng
  • Johan Lim
  • Kyeong Lee
  • Donghyeon Yu
  • Sujung Choi

Abstract

We propose an algorithm to sample the area of the smallest convex hull containing $$n$$ n sample points uniformly distributed over unit square. To do it, we introduce a new coordinate system for the position of vertexes and re-write joint distribution of the number of vertexes and their locations in the new coordinate system. The proposed algorithm is much faster than existing procedure and has a computational complexity on the order of $$O(T)$$ O ( T ) , where $$T$$ T is the number of vertexes. Using the proposed algorithm, we numerically investigate the asymptotic behavior of functionals of the random convex hull. In addition, we apply it to finding pairs of stocks where the returns are dependent on each other on the New York Stock Exchange. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Chi Ng & Johan Lim & Kyeong Lee & Donghyeon Yu & Sujung Choi, 2014. "A fast algorithm to sample the number of vertexes and the area of the random convex hull on the unit square," Computational Statistics, Springer, vol. 29(5), pages 1187-1205, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:1187-1205
    DOI: 10.1007/s00180-014-0486-1
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    References listed on IDEAS

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    1. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    2. Zani, Sergio & Riani, Marco & Corbellini, Aldo, 1998. "Robust bivariate boxplots and multiple outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 28(3), pages 257-270, September.
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