IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v182y2022ics0167715221002601.html
   My bibliography  Save this article

Generalizations of some concentration inequalities

Author

Listed:
  • Bhat, M. Ashraf
  • Kosuru, G. Sankara Raju

Abstract

For a real-valued measurable function f and a nonnegative, nondecreasing function ϕ, we first obtain a Chebyshev type inequality which provides an upper bound for ϕ(λ1)μ({x∈Ω:f(x)≥λ1})+∑k=2nϕ(λk)−ϕ(λk−1)μ({x∈Ω:f(x)≥λk}), where 0<λ1<λ2<⋯<λn<∞. Using this, generalizations of a few concentration inequalities such as Markov, reverse Markov, Bienaymé–Chebyshev, Cantelli and Hoeffding inequalities are obtained.

Suggested Citation

  • Bhat, M. Ashraf & Kosuru, G. Sankara Raju, 2022. "Generalizations of some concentration inequalities," Statistics & Probability Letters, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:stapro:v:182:y:2022:i:c:s0167715221002601
    DOI: 10.1016/j.spl.2021.109298
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221002601
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109298?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. Haruhiko Ogasawara, 2019. "The multiple Cantelli inequalities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 495-506, September.
    2. Haruhiko Ogasawara, 2021. "Improvements of the Markov and Chebyshev inequalities using the partial expectation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(1), pages 116-131, January.
    3. Haruhiko Ogasawara, 2020. "The multivariate Markov and multiple Chebyshev inequalities," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(2), pages 441-453, January.
    4. Eisenberg, Bennett & Ghosh, B. K., 2001. "A generalization of Markov's inequality," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 59-65, May.
    5. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    6. Budny, Katarzyna, 2014. "A generalization of Chebyshev’s inequality for Hilbert-space-valued random elements," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 62-65.
    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. Roxana A. Ion & Chris A. J. Klaassen & Edwin R. van den Heuvel, 2023. "Sharp inequalities of Bienaymé–Chebyshev and Gauß type for possibly asymmetric intervals around the mean," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 566-601, June.

    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. Roxana A. Ion & Chris A. J. Klaassen & Edwin R. van den Heuvel, 2023. "Sharp inequalities of Bienaymé–Chebyshev and Gauß type for possibly asymmetric intervals around the mean," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 566-601, June.
    2. Stevanovic Dalibor, 2016. "Common time variation of parameters in reduced-form macroeconomic models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(2), pages 159-183, April.
    3. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    4. A. Fadlelmawla & M. Al-Otaibi, 2005. "Analysis of the Water Resources Status in Kuwait," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 19(5), pages 555-570, October.
    5. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    6. Duan, Jinyun & Li, Chenwei & Xu, Yue & Wu, Chia-Huei, 2017. "Transformational leadership and employee voice behavior: a Pygmalion mechanism," LSE Research Online Documents on Economics 68035, London School of Economics and Political Science, LSE Library.
    7. Mammassis, Constantinos S. & Kostopoulos, Konstantinos C., 2019. "CEO goal orientations, environmental dynamism and organizational ambidexterity: An investigation in SMEs," European Management Journal, Elsevier, vol. 37(5), pages 577-588.
    8. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    9. Jugend, Daniel & da Silva, Sérgio Luis & Salgado, Manoel Henrique & Miguel, Paulo Augusto Cauchick, 2016. "Product portfolio management and performance: Evidence from a survey of innovative Brazilian companies," Journal of Business Research, Elsevier, vol. 69(11), pages 5095-5100.
    10. Ian Maitland & Mitsuhiro Umezu, 2006. "An Evaluation of Japan's Stakeholder Capitalism," Journal of Private Enterprise, The Association of Private Enterprise Education, vol. 22(Spring 20), pages 131-164.
    11. Craig Loschmann & Özge Bilgili & Melissa Siegel, 2019. "Considering the benefits of hosting refugees: evidence of refugee camps influencing local labour market activity and economic welfare in Rwanda," IZA Journal of Migration and Development, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 9(1), pages 1-23, December.
    12. Dimitris Bertsimas & Agni Orfanoudaki, 2021. "Algorithmic Insurance," Papers 2106.00839, arXiv.org, revised Dec 2022.
    13. Walter Murray & Tomás Tinoco De Rubira & Adam Wigington, 2015. "A robust and informative method for solving large-scale power flow problems," Computational Optimization and Applications, Springer, vol. 62(2), pages 431-475, November.
    14. Rafael Epstein & Andres Neely & Andres Weintraub & Fernando Valenzuela & Sergio Hurtado & Guillermo Gonzalez & Alex Beiza & Mauricio Naveas & Florencio Infante & Fernando Alarcon & Gustavo Angulo & Cr, 2012. "A Strategic Empty Container Logistics Optimization in a Major Shipping Company," Interfaces, INFORMS, vol. 42(1), pages 5-16, February.
    15. Hilfer, R., 2006. "Macroscopic capillarity without a constitutive capillary pressure function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 209-225.
    16. Abdel-Latif Abla & Schmitz Hubert, 2010. "Growth Alliances: Insights from Egypt," Business and Politics, De Gruyter, vol. 12(4), pages 1-29, December.
    17. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    18. Abdelmoety, Ziad Hassan & Aboul-Dahab, Sameh & Agag, Gomaa, 2022. "A cross cultural investigation of retailers commitment to CSR and customer citizenship behaviour: The role of ethical standard and value relevance," Journal of Retailing and Consumer Services, Elsevier, vol. 64(C).
    19. Hamed Mamani & Shima Nassiri & Michael R. Wagner, 2017. "Closed-Form Solutions for Robust Inventory Management," Management Science, INFORMS, vol. 63(5), pages 1625-1643, May.
    20. M. Bergounioux, 2016. "Mathematical Analysis of a Inf-Convolution Model for Image Processing," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 1-21, January.

    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:182:y:2022:i:c:s0167715221002601. 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.