IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v166y2018icp212-224.html
   My bibliography  Save this article

Efron’s monotonicity property for measures on R2

Author

Listed:
  • Saumard, Adrien
  • Wellner, Jon A.

Abstract

In this paper, we prove some kernel representations for the covariance of two functions taken on the same random variable and we deduce kernel representations for some functionals of a continuous one-dimensional measure. Then we apply these formulas to extend Efron’s monotonicity property, given in Efron (1965) and valid for independent log-concave measures, to the case of general measures on R2. The new formulas are also used to derive some further quantitative estimates in Efron’s monotonicity property.

Suggested Citation

  • Saumard, Adrien & Wellner, Jon A., 2018. "Efron’s monotonicity property for measures on R2," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 212-224.
    • Handle: RePEc:eee:jmvana:v:166:y:2018:i:c:p:212-224
    DOI: 10.1016/j.jmva.2018.03.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X17304281
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2018.03.005?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. Hu, Taizhong & Hu, Jinjin, 1999. "Sufficient conditions for negative association of random variables," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 167-173, November.
    2. Zengri Wang, 2003. "Matching conditional and marginal shapes in binary random intercept models using a bridge distribution function," Biometrika, Biometrika Trust, vol. 90(4), pages 765-775, December.
    3. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    4. J. George Shanthikumar & David D. Yao, 1987. "Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks," Operations Research, INFORMS, vol. 35(4), pages 583-588, August.
    5. Florian Ederer, 2010. "Feedback and Motivation in Dynamic Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(3), pages 733-769, September.
    6. Hwang, Gene T. & Stefanski, Leonard A., 1994. "Monotonicity of regression functions in structural measurement error models," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 113-116, May.
    7. Rinott, Yosef & Samuel-Cahn, Ester, 1991. "Orderings of optimal stopping values and prophet inequalities for certain multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 104-114, April.
    8. Johnson, Oliver, 2007. "Log-concavity and the maximum entropy property of the Poisson distribution," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 791-802, June.
    9. Yoav Benjamini & Ruth Heller, 2008. "Screening for Partial Conjunction Hypotheses," Biometrics, The International Biometric Society, vol. 64(4), pages 1215-1222, December.
    10. Yasushi Masuda, 1995. "Exploiting Partial Information in Queueing Systems," Operations Research, INFORMS, vol. 43(3), pages 530-536, June.
    11. Zhuang, Weiwei & Yao, Junchao & Hu, Taizhong, 2010. "Conditional ordering of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 640-644, March.
    12. Block, Henry W. & Savits, Thomas H. & Shaked, Moshe, 1985. "A concept of negative dependence using stochastic ordering," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 81-86, April.
    13. Boland, Philip J. & Hollander, Myles & Joag-Dev, Kumar & Kochar, Subhash, 1996. "Bivariate Dependence Properties of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 75-89, January.
    14. Ma, Chunsheng, 1999. "On the posterior distribution of a location parameter from a strongly unimodal distribution," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 33-37, March.
    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. Denuit, Michel & Robert, Christian Y., 2023. "From risk reduction to risk elimination by conditional mean risk sharing of independent losses," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 46-59.

    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. Franco Pellerey & Jorge Navarro, 2022. "Stochastic monotonicity of dependent variables given their sum," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 543-561, June.
    2. Daduna, Hans & Szekli, Ryszard, 1996. "A queueing theoretical proof of increasing property of Polya frequency functions," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 233-242, February.
    3. Anja Schöttner & Veikko Thiele, 2010. "Promotion Tournaments and Individual Performance Pay," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(3), pages 699-731, September.
    4. Zhuang, Weiwei & Yao, Junchao & Hu, Taizhong, 2010. "Conditional ordering of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 640-644, March.
    5. Chateauneuf, Alain & Mostoufi, Mina & Vyncke, David, 2015. "Multivariate risk sharing and the derivation of individually rational Pareto optima," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 73-78.
    6. Gwen-Jiro Clochard & Guillaume Hollard & Julia Wirtz, 2022. "More effort or better technologies? On the effect of relative performance feedback," Bristol Economics Discussion Papers 22/767, School of Economics, University of Bristol, UK.
    7. Denter, Philipp & Sisak, Dana, 2015. "Do polls create momentum in political competition?," Journal of Public Economics, Elsevier, vol. 130(C), pages 1-14.
    8. Clare Leaver & Gian Luigi Albano & University College London and ELSE, 2004. "Transparency, Recruitment and Retention in the Public Sector," Economics Series Working Papers 219, University of Oxford, Department of Economics.
    9. Tim J. Boonen & Wing Fung Chong & Mario Ghossoub, 2024. "Pareto‐efficient risk sharing in centralized insurance markets with application to flood risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 91(2), pages 449-488, June.
    10. Denuit, Michel & Hieber, Peter & Robert, Christian Y., 2021. "Mortality credits within large survivor funds," LIDAM Discussion Papers ISBA 2021038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Delfgaauw, Josse & Dur, Robert & Non, Arjan & Verbeke, Willem, 2014. "Dynamic incentive effects of relative performance pay: A field experiment," Labour Economics, Elsevier, vol. 28(C), pages 1-13.
    12. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    13. Anil Arya & Brian Mittendorf, 2011. "The Benefits of Aggregate Performance Metrics in the Presence of Career Concerns," Management Science, INFORMS, vol. 57(8), pages 1424-1437, August.
    14. repec:ipg:wpaper:2014-074 is not listed on IDEAS
    15. Müller, Alfred, 2001. "Bounds for optimal stopping values of dependent random variables with given marginals," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 73-78, March.
    16. De Paola, Maria & Scoppa, Vincenzo, 2011. "Frequency of examinations and student achievement in a randomized experiment," Economics of Education Review, Elsevier, vol. 30(6), pages 1416-1429.
    17. Jan Zabojnik, 2011. "Subjective Evaluations With Performance Feedback," Working Paper 1283, Economics Department, Queen's University.
    18. Shinya Kajitani & Keiichi Morimoto & Shiba Suzuki, 2020. "Information feedback in relative grading: Evidence from a field experiment," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-19, April.
    19. Jason Roy & Michael J. Daniels, 2008. "A General Class of Pattern Mixture Models for Nonignorable Dropout with Many Possible Dropout Times," Biometrics, The International Biometric Society, vol. 64(2), pages 538-545, June.
    20. Fallou Niakh, 2023. "A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules," Papers 2303.05421, arXiv.org, revised Jul 2023.
    21. Denuit, Michel & Robert, Christian Y., 2021. "Efron’s asymptotic monotonicity property in the Gaussian stable domain of attraction," Journal of Multivariate Analysis, Elsevier, vol. 186(C).

    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:jmvana:v:166:y:2018:i:c:p:212-224. 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.