IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v127y2018icp96-115.html
   My bibliography  Save this article

Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population

Author

Listed:
  • Giguelay, J.
  • Huet, S.

Abstract

The development of nonparametric procedures for testing shape constraint (monotonicity, convexity, unimodality, etc.) has received increasing interest. Nevertheless, testing the k-monotonicity of a discrete density for k larger than 2 has received little attention. To deal with this issue, several testing procedures based on the empirical distribution of the observations have been developed. They are non-parametric, easy to implement and proven to be asymptotically of the desired level and consistent. An estimator of the degree of k-monotonicity of the distribution is presented. An application to the estimation of the total number of classes in a population is proposed. A large simulation study makes it possible to assess the performances of the various procedures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:96-115
    DOI: 10.1016/j.csda.2018.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318300458
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.02.006?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. repec:dau:papers:123456789/11474 is not listed on IDEAS
    2. Cécile Durot & Sylvie Huet & François Koladjo & Stéphane Robin, 2015. "Nonparametric species richness estimation under convexity constraint," Environmetrics, John Wiley & Sons, Ltd., vol. 26(7), pages 502-513, November.
    3. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.
    4. Fadoua Balabdaoui & Jon A. Wellner, 2010. "Estimation of a k‐monotone density: characterizations, consistency and minimax lower bounds," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 45-70, February.
    5. Groeneboom,Piet & Jongbloed,Geurt, 2014. "Nonparametric Estimation under Shape Constraints," Cambridge Books, Cambridge University Press, number 9780521864015.
    6. Chee, Chew-Seng & Wang, Yong, 2016. "Nonparametric estimation of species richness using discrete k-monotone distributions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 107-118.
    7. Fadoua Balabdaoui & Hanna Jankowski & Kaspar Rufibach & Marios Pavlides, 2013. "Asymptotics of the discrete log-concave maximum likelihood estimator and related applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 769-790, September.
    8. Durot, Cécile & Huet, Sylvie & Koladjo, François & Robin, Stéphane, 2013. "Least-squares estimation of a convex discrete distribution," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 282-298.
    9. Balabdaoui, Fadoua & Durot, Cécile, 2015. "Marshall lemma in discrete convex estimation," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 143-148.
    10. repec:dau:papers:123456789/4650 is not listed on IDEAS
    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. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

    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. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    2. Balabdaoui, Fadoua & Durot, Cécile & Koladjo, Babagnidé François, 2018. "Testing convexity of a discrete distribution," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 8-13.
    3. Mao, Lu, 2022. "Identification of the outcome distribution and sensitivity analysis under weak confounder–instrument interaction," Statistics & Probability Letters, Elsevier, vol. 189(C).
    4. 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.
    5. 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.
    6. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    7. 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.
    8. Seungchul Baek & Junyong Park, 2022. "A computationally efficient approach to estimating species richness and rarefaction curve," Computational Statistics, Springer, vol. 37(4), pages 1919-1941, September.
    9. 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.
    10. 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.
    11. 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.
    12. José E. Chacón, 2020. "The Modal Age of Statistics," International Statistical Review, International Statistical Institute, vol. 88(1), pages 122-141, April.
    13. 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.
    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. 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.
    17. 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.
    18. Denuit, Michel & Liu, Liqun & Meyer, Jack, 2014. "A separation theorem for the weak s-convex orders," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 279-284.
    19. Balabdaoui, Fadoua & Durot, Cécile, 2015. "Marshall lemma in discrete convex estimation," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 143-148.
    20. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.

    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:csdana:v:127:y:2018:i:c:p:96-115. 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/locate/csda .

    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.