IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v29y2016i2d10.1007_s10959-014-0572-x.html
   My bibliography  Save this article

A Multivalued Strong Law of Large Numbers

Author

Listed:
  • Pedro Terán

    (Universidad de Oviedo)

Abstract

We prove a strong law of large numbers for random closed sets in a separable Banach space. It improves upon and unifies the laws of large numbers with convergence in the Wijsman, Mosco and slice topologies, without requiring extra assumptions on either the properties of the space or the kind of sets that can be taken on by the random set as values.

Suggested Citation

  • Pedro Terán, 2016. "A Multivalued Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 29(2), pages 349-358, June.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0572-x
    DOI: 10.1007/s10959-014-0572-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-014-0572-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-014-0572-x?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. Zvi Artstein & Sergiu Hart, 1981. "Law of Large Numbers for Random Sets and Allocation Processes," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 485-492, November.
    2. Pedro Terán & Ilya Molchanov, 2006. "The Law of Large Numbers in a Metric Space with a Convex Combination Operation," Journal of Theoretical Probability, Springer, vol. 19(4), pages 875-898, December.
    3. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    4. Hess, Christian, 1991. "On multivalued martingales whose values may be unbounded: martingale selectors and mosco convergence," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 175-201, October.
    5. Jérôme Couvreux & Christian Hess, 1999. "A Lévy Type Martingale Convergence Theorem for Random Sets with Unbounded Values," Journal of Theoretical Probability, Springer, vol. 12(4), pages 933-969, October.
    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. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    2. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP63/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    4. Donald S. Poskitt & Xueyan Zhao, 2023. "Bootstrap Hausdorff Confidence Regions for Average Treatment Effect Identified Sets," Monash Econometrics and Business Statistics Working Papers 9/23, Monash University, Department of Econometrics and Business Statistics.
    5. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    6. Karun Adusumilli & Taisuke Otsu, 2017. "Empirical Likelihood for Random Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1064-1075, July.
    7. Zhiwei Zhang, 2010. "Profile Likelihood and Incomplete Data," International Statistical Review, International Statistical Institute, vol. 78(1), pages 102-116, April.
    8. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    9. Arun G. Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2019. "Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap," NBER Working Papers 25593, National Bureau of Economic Research, Inc.
    10. Kaval, K. & Molchanov, I., 2006. "Link-save trading," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 710-728, September.
    11. Nicky L. Grant & Richard J. Smith, 2018. "GEL-based inference with unconditional moment inequality restrictions," CeMMAP working papers CWP23/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Yuan Liao & Anna Simoni, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," Papers 1212.3267, arXiv.org, revised Nov 2013.
    13. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    14. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    15. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    16. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    17. Bontemps, Christian & Kumar, Rohit, 2020. "A geometric approach to inference in set-identified entry games," Journal of Econometrics, Elsevier, vol. 218(2), pages 373-389.
    18. Ho, Kate & Rosen, Adam M., 2015. "Partial Identification in Applied Research: Benefits and Challenges," CEPR Discussion Papers 10883, C.E.P.R. Discussion Papers.
    19. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2014. "Inference for functions of partially identified parameters in moment inequality models," CeMMAP working papers 22/14, Institute for Fiscal Studies.
    20. Komunjer, Ivana, 2007. "Global Identification In Nonlinear Semiparametric Models," University of California at San Diego, Economics Working Paper Series qt8dk0n386, Department of Economics, UC San Diego.
    21. Quang, Nguyen Van & Giap, Duong Xuan, 2013. "Mosco convergence of SLLN for triangular arrays of rowwise independent random sets," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1117-1126.

    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:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0572-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.