IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v81y2019i2d10.1007_s13171-018-0147-5.html
   My bibliography  Save this article

Empirical Priors and Posterior Concentration Rates for a Monotone Density

Author

Listed:
  • Ryan Martin

    (North Carolina State University)

Abstract

In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are not satisfied. In this paper, I first develop a new prior designed specifically to satisfy an empirical version of the prior concentration property, and then I give sufficient conditions on the prior inputs such that the corresponding empirical Bayes posterior concentrates around the true monotone density at nearly the optimal minimax rate. Numerical illustrations also reveal the practical benefits of the proposed empirical Bayes approach compared to Dirichlet process mixtures.

Suggested Citation

  • Ryan Martin, 2019. "Empirical Priors and Posterior Concentration Rates for a Monotone Density," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 493-509, December.
    • Handle: RePEc:spr:sankha:v:81:y:2019:i:2:d:10.1007_s13171-018-0147-5
    DOI: 10.1007/s13171-018-0147-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-018-0147-5
    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/s13171-018-0147-5?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. Vytaras Brazauskas & Andreas Kleefeld, 2016. "Modeling Severity and Measuring Tail Risk of Norwegian Fire Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(1), pages 1-16, January.
    2. Groeneboom,Piet & Jongbloed,Geurt, 2014. "Nonparametric Estimation under Shape Constraints," Cambridge Books, Cambridge University Press, number 9780521864015.
    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. Mao, Lu, 2022. "Identification of the outcome distribution and sensitivity analysis under weak confounder–instrument interaction," Statistics & Probability Letters, Elsevier, vol. 189(C).
    2. Ruixuan Liu & Zhengfei Yu, 2019. "Simple Semiparametric Estimation of Ordered Response Models: with an Application to the Interdependence Duration Models," Tsukuba Economics Working Papers 2019-004, Faculty of Humanities and Social Sciences, University of Tsukuba.
    3. Yoici Arai & Taisuke Otsu & Mengshan Xu, 2022. "GLS under monotone heteroskedasticity," STICERD - Econometrics Paper Series 625, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    5. Piet Groeneboom, 2021. "Estimation of the incubation time distribution for COVID‐19," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 161-179, May.
    6. Elina Robeva & Bernd Sturmfels & Ngoc Tran & Caroline Uhler, 2021. "Maximum likelihood estimation for totally positive log‐concave densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 817-844, September.
    7. Hendrik P. Lopuhaä & Eni Musta, 2017. "Smooth estimation of a monotone hazard and a monotone density under random censoring," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(1), pages 58-82, January.
    8. Xu, Mengshan & Otsu, Taisuke, 2020. "Score estimation of monotone partially linear index model," LSE Research Online Documents on Economics 106698, London School of Economics and Political Science, LSE Library.
    9. José E. Chacón, 2020. "The Modal Age of Statistics," International Statistical Review, International Statistical Institute, vol. 88(1), pages 122-141, April.
    10. Bowen Liu & Malwane M. A. Ananda, 2022. "A Generalized Family of Exponentiated Composite Distributions," Mathematics, MDPI, vol. 10(11), pages 1-18, June.
    11. Giguelay, J. & Huet, S., 2018. "Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 96-115.
    12. Taisuke Otsu & Mengshan Xu, 2019. "Score estimation of monotone partially linear index model," STICERD - Econometrics Paper Series 603, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2023. "Hidden semi-Markov models for rainfall-related insurance claims," Discussion Papers 2023/17, Norwegian School of Economics, Department of Business and Management Science.
    14. Xi Chen & Victor Chernozhukov & Iv'an Fern'andez-Val & Scott Kostyshak & Ye Luo, 2018. "Shape-Enforcing Operators for Point and Interval Estimators," Papers 1809.01038, arXiv.org, revised Feb 2021.
    15. Sungwook Kim & Michael P. Fay & Michael A. Proschan, 2021. "Valid and approximately valid confidence intervals for current status data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 438-452, July.
    16. Reynkens, Tom & Verbelen, Roel & Beirlant, Jan & Antonio, Katrien, 2017. "Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 65-77.
    17. Queensley C. Chukwudum, 2019. "Reinsurance Pricing of Large Motor Insurance Claims in Nigeria: An Extreme Value Analysis," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(4), pages 1-12, July.
    18. Yuguang Fan & Philip S. Griffin & Ross Maller & Alexander Szimayer & Tiandong Wang, 2017. "The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation," Risks, MDPI, vol. 5(1), pages 1-27, January.
    19. Quan Li & Xin Wang & Shuaiang Rong, 2018. "Probabilistic Load Flow Method Based on Modified Latin Hypercube-Important Sampling," Energies, MDPI, vol. 11(11), pages 1-14, November.
    20. Lu Mao & Dan-Yu Lin & Donglin Zeng, 2017. "Semiparametric regression analysis of interval-censored competing risks data," Biometrics, The International Biometric Society, vol. 73(3), pages 857-865, 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:spr:sankha:v:81:y:2019:i:2:d:10.1007_s13171-018-0147-5. 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.