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Many multivariate records

Author

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  • Goldie, Charles M.
  • Resnick, Sidney I.

Abstract

(Xn)n=1,2,... is a sequence of independent, identically distributed random vectors in 2. Say Xn is a record if there is a record simultaneously in both coordinates at index n. The total number of records of a sequence is frequently finite so we consider the behaviour of the records in a fixed rectangle A conditional on there being a large number of records NA in the rectangle. We join the records up to form a random parametrized curve, and prove that, under suitable conditions, as the number of records in the rectangle goes to infinity the random curves converge conditionally in probability to a non-random limit parametrized curve, which we characterize. We also prove a large-deviation result for the random curves.

Suggested Citation

  • Goldie, Charles M. & Resnick, Sidney I., 1995. "Many multivariate records," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 185-216, October.
    • Handle: RePEc:eee:spapps:v:59:y:1995:i:2:p:185-216
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    References listed on IDEAS

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    1. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
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    Cited by:

    1. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
    2. Ismihan Bayramoglu, 2016. "On the records of multivariate random sequences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 725-747, August.
    3. Nayak, S. S. & Zalki, Madhusudhan, 2001. "Almost sure limit points of record values from two independent populations," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 181-187, January.
    4. N. Balakrishnan & A. Stepanov & V. B. Nevzorov, 2020. "North-east bivariate records," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 961-976, November.
    5. Clément Dombry & Michael Falk & Maximilian Zott, 2019. "On Functional Records and Champions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1252-1277, September.
    6. Gnedin, A.V.Alexander V., 2004. "Best choice from the planar Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 317-354, June.

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