IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v199y2023ics0167715223000718.html
   My bibliography  Save this article

A phase transition for the probability of being a maximum among random vectors with general iid coordinates

Author

Listed:
  • Jacobovic, Royi
  • Zuk, Or

Abstract

Consider n iid real-valued random vectors of size k having iid coordinates with a general distribution function F. A vector is a maximum if and only if there is no other vector in the sample that weakly dominates it in all coordinates. Let pk,n be the probability that the first vector is a maximum. The main result of the present paper is that if k≡kn grows at a slower (faster) rate than a certain factor of log(n), then pk,n→0 (resp. pk,n→1) as n→∞. Furthermore, the factor is fully characterized as a functional of F. We also study the effect of F on pk,n, showing that while pk,n may be highly affected by the choice of F, the phase transition is the same for all distribution functions up to a constant factor.

Suggested Citation

  • Jacobovic, Royi & Zuk, Or, 2023. "A phase transition for the probability of being a maximum among random vectors with general iid coordinates," Statistics & Probability Letters, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:stapro:v:199:y:2023:i:c:s0167715223000718
    DOI: 10.1016/j.spl.2023.109847
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715223000718
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2023.109847?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Gérard Biau & Erwan Scornet, 2016. "A random forest guided tour," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 197-227, June.
    2. Gérard Biau & Erwan Scornet, 2016. "Rejoinder on: A random forest guided tour," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 264-268, June.
    Full references (including those not matched with items on IDEAS)

    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. Hou, Lei & Elsworth, Derek & Zhang, Fengshou & Wang, Zhiyuan & Zhang, Jianbo, 2023. "Evaluation of proppant injection based on a data-driven approach integrating numerical and ensemble learning models," Energy, Elsevier, vol. 264(C).
    2. Ma, Zhikai & Huo, Qian & Wang, Wei & Zhang, Tao, 2023. "Voltage-temperature aware thermal runaway alarming framework for electric vehicles via deep learning with attention mechanism in time-frequency domain," Energy, Elsevier, vol. 278(C).
    3. Patrick Krennmair & Timo Schmid, 2022. "Flexible domain prediction using mixed effects random forests," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1865-1894, November.
    4. Manuel J. García Rodríguez & Vicente Rodríguez Montequín & Francisco Ortega Fernández & Joaquín M. Villanueva Balsera, 2019. "Public Procurement Announcements in Spain: Regulations, Data Analysis, and Award Price Estimator Using Machine Learning," Complexity, Hindawi, vol. 2019, pages 1-20, November.
    5. Sachin Kumar & Zairu Nisha & Jagvinder Singh & Anuj Kumar Sharma, 2022. "Sensor network driven novel hybrid model based on feature selection and SVR to predict indoor temperature for energy consumption optimisation in smart buildings," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(6), pages 3048-3061, December.
    6. Escribano, Álvaro & Wang, Dandan, 2021. "Mixed random forest, cointegration, and forecasting gasoline prices," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1442-1462.
    7. Yigit Aydede & Jan Ditzen, 2022. "Identifying the regional drivers of influenza-like illness in Nova Scotia with dominance analysis," Papers 2212.06684, arXiv.org.
    8. Siyoon Kwon & Hyoseob Noh & Il Won Seo & Sung Hyun Jung & Donghae Baek, 2021. "Identification Framework of Contaminant Spill in Rivers Using Machine Learning with Breakthrough Curve Analysis," IJERPH, MDPI, vol. 18(3), pages 1-26, January.
    9. Yan, Ran & Wang, Shuaian & Du, Yuquan, 2020. "Development of a two-stage ship fuel consumption prediction and reduction model for a dry bulk ship," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    10. Yi Cao & Xue Li, 2022. "Multi-Model Attention Fusion Multilayer Perceptron Prediction Method for Subway OD Passenger Flow under COVID-19," Sustainability, MDPI, vol. 14(21), pages 1-16, November.
    11. Filmer,Deon P. & Nahata,Vatsal & Sabarwal,Shwetlena, 2021. "Preparation, Practice, and Beliefs : A Machine Learning Approach to Understanding Teacher Effectiveness," Policy Research Working Paper Series 9847, The World Bank.
    12. Boller, Daniel & Lechner, Michael & Okasa, Gabriel, 2021. "The Effect of Sport in Online Dating: Evidence from Causal Machine Learning," Economics Working Paper Series 2104, University of St. Gallen, School of Economics and Political Science.
    13. Jorge Antunes & Peter Wanke & Thiago Fonseca & Yong Tan, 2023. "Do ESG Risk Scores Influence Financial Distress? Evidence from a Dynamic NDEA Approach," Sustainability, MDPI, vol. 15(9), pages 1-32, May.
    14. Lyudmyla Kirichenko & Tamara Radivilova & Vitalii Bulakh, 2018. "Machine Learning in Classification Time Series with Fractal Properties," Data, MDPI, vol. 4(1), pages 1-13, December.
    15. Ivan Brandić & Lato Pezo & Nikola Bilandžija & Anamarija Peter & Jona Šurić & Neven Voća, 2023. "Comparison of Different Machine Learning Models for Modelling the Higher Heating Value of Biomass," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    16. José A. Ferreira, 2022. "Models under which random forests perform badly; consequences for applications," Computational Statistics, Springer, vol. 37(4), pages 1839-1854, September.
    17. Villacis, Alexis & Badruddoza, Syed & Mayorga, Joaquin & Mishra, Ashok K., 2022. "Using Machine Learning to Test the Consistency of Food Insecurity Measures," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322472, Agricultural and Applied Economics Association.
    18. Valeria D’Amato & Rita D’Ecclesia & Susanna Levantesi, 2022. "ESG score prediction through random forest algorithm," Computational Management Science, Springer, vol. 19(2), pages 347-373, June.
    19. Pourkhanali, Armin & Khezr, Peyman & Nepal, Rabindra & Jamasb, Tooraj, 2024. "Navigating the crisis: Fuel price caps in the Australian national wholesale electricity market," Energy Economics, Elsevier, vol. 129(C).
    20. Raman Pall & Yvan Gauthier & Sofia Auer & Walid Mowaswes, 2023. "Predicting drug shortages using pharmacy data and machine learning," Health Care Management Science, Springer, vol. 26(3), pages 395-411, September.

    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:stapro:v:199:y:2023:i:c:s0167715223000718. 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/622892/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.