IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v59y1995i2p185-216.html
   My bibliography  Save this article

Many multivariate records

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(95)00047-B
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Clément Dombry & Michael Falk & Maximilian Zott, 2019. "On Functional Records and Champions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1252-1277, September.
    5. 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.
    6. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stilian A. Stoev & Murad S. Taqqu, 2007. "Limit Theorems for Sums of Heavy-tailed Variables with Random Dependent Weights," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 55-87, March.
    2. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    3. Anatolii A. Puhalskii, 2003. "On Large Deviation Convergence of Invariant Measures," Journal of Theoretical Probability, Springer, vol. 16(3), pages 689-724, July.
    4. Saulius Minkevičius & Igor Katin & Joana Katina & Irina Vinogradova-Zinkevič, 2021. "On Little’s Formula in Multiphase Queues," Mathematics, MDPI, vol. 9(18), pages 1-15, September.
    5. Doruk Cetemen & Can Urgun & Leeat Yariv, 2023. "Collective Progress: Dynamics of Exit Waves," Journal of Political Economy, University of Chicago Press, vol. 131(9), pages 2402-2450.
    6. Zhang, Tonglin, 2024. "Variables selection using L0 penalty," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    7. Cetemen, Doruk & Hwang, Ilwoo & Kaya, Ayça, 2020. "Uncertainty-driven cooperation," Theoretical Economics, Econometric Society, vol. 15(3), July.
    8. Stefan Ankirchner & Christophette Blanchet-Scalliet & Nabil Kazi-Tani, 2019. "The De Vylder-Goovaerts conjecture holds true within the diffusion limit," Post-Print hal-01887402, HAL.
    9. Penrose, Mathew D., 2000. "Central limit theorems for k-nearest neighbour distances," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 295-320, February.
    10. Grégoire, Gérard & Hamrouni, Zouhir, 2002. "Change Point Estimation by Local Linear Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 56-83, October.
    11. Ralescu, Stefan S. & Puri, Madan L., 1996. "Weak convergence of sequences of first passage processes and applications," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 327-345, July.
    12. Scalas, Enrico & Viles, Noèlia, 2014. "A functional limit theorem for stochastic integrals driven by a time-changed symmetric α-stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 385-410.
    13. Avishai Mandelbaum & Petar Momčilović, 2008. "Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 561-586, August.
    14. Gromoll, H. Christian & Terwilliger, Bryce & Zwart, Bert, 2020. "Heavy traffic limit for the workload plateau process in a tandem queue with identical service times," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1435-1460.
    15. Tyran-Kaminska, Marta, 2010. "Convergence to Lévy stable processes under some weak dependence conditions," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1629-1650, August.
    16. Gianmarco Bet & Remco van der Hofstad & Johan S. H. van Leeuwaarden, 2019. "Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 821-864, August.
    17. G. Bet, 2020. "An alternative approach to heavy-traffic limits for finite-pool queues," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 121-144, June.
    18. Dijk, N.M. van, 1991. "On uniformization for nonhomogeneous Markov chains," Serie Research Memoranda 0006, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    19. Ansgar Steland, 2016. "Asymptotics for random functions moderated by dependent noise," Statistical Inference for Stochastic Processes, Springer, vol. 19(3), pages 363-387, October.
    20. Choudhary Pankaj K, 2010. "A Unified Approach for Nonparametric Evaluation of Agreement in Method Comparison Studies," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-26, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:59:y:1995:i:2:p:185-216. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.