IDEAS home Printed from https://ideas.repec.org/a/wly/envmet/v31y2020i8ne2645.html
   My bibliography  Save this article

Functional estimation of diversity profiles

Author

Listed:
  • Francesca Fortuna
  • Stefano Antonio Gattone
  • Tonio Di Battista

Abstract

It is well known that the diversity profile provides a complete picture about the evenness of the relative abundance distribution of an ecological population. This complexity measure is a continuous function evaluated on a suitable grid of values x ≥ 0 that determine the measure's sensitivity to the most dominant species. In this paper, a functional design‐based estimation of diversity profiles is developed by applying a framework based on functional data analysis (FDA). These curves, which are positive, decreasing, and convex, can be viewed as constrained functional data. Therefore, a naive direct application of the FDA methodology can be misleading, both theoretically and practically. To tackle this problem, the diversity profile is defined in terms of a differential equation, in such a manner that the function to be estimated is unconstrained. An approximation of the bias and the variance of the estimator is derived using the delta method. The accuracy of the proposed functional constrained estimator is evaluated through a simulation study. The procedure is also applied on a real dataset concerning tree stem diameter diversity.

Suggested Citation

  • Francesca Fortuna & Stefano Antonio Gattone & Tonio Di Battista, 2020. "Functional estimation of diversity profiles," Environmetrics, John Wiley & Sons, Ltd., vol. 31(8), December.
    • Handle: RePEc:wly:envmet:v:31:y:2020:i:8:n:e2645
    DOI: 10.1002/env.2645
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/env.2645
    Download Restriction: no
    File URL: https://libkey.io/10.1002/env.2645?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
    ---><---

    References listed on IDEAS

    as
    1. J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    2. Bongiorno, Enea G. & Goia, Aldo, 2019. "Describing the concentration of income populations by functional principal component analysis on Lorenz curves," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 10-24.
    3. Stefano A. Gattone & Tonio Di Battista, 2009. "A functional approach to diversity profiles," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(2), pages 267-284, May.
    4. L. Barabesi & L. Fattorini & M. Marcheselli & C. Pisani & L. Pratelli, 2015. "The estimation of diversity indexes by using stratified allocations of plots, points or transects," Environmetrics, John Wiley & Sons, Ltd., vol. 26(3), pages 202-215, May.
    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. Luke Durell & J. Thad Scott & Douglas Nychka & Amanda S. Hering, 2023. "Functional forecasting of dissolved oxygen in high‐frequency vertical lake profiles," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    2. Trevor Harris & Bo Li & J. Derek Tucker, 2022. "Scalable multiple changepoint detection for functional data sequences," Environmetrics, John Wiley & Sons, Ltd., vol. 33(2), March.
    3. Gattone, Stefano Antonio & Fortuna, Francesca & Evangelista, Adelia & Di Battista, Tonio, 2022. "Simultaneous confidence bands for the functional mean of convex curves," Econometrics and Statistics, Elsevier, vol. 24(C), pages 183-193.
    4. J. Derek Tucker & Drew Yarger, 2024. "Elastic functional changepoint detection of climate impacts from localized sources," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.

    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. Gattone, Stefano Antonio & Fortuna, Francesca & Evangelista, Adelia & Di Battista, Tonio, 2022. "Simultaneous confidence bands for the functional mean of convex curves," Econometrics and Statistics, Elsevier, vol. 24(C), pages 183-193.
    2. Charu Sharma & Amber Habib & Sunil Bowry, 2018. "Cluster analysis of stocks using price movements of high frequency data from National Stock Exchange," Papers 1803.09514, arXiv.org.
    3. Shively, Thomas S. & Kockelman, Kara & Damien, Paul, 2010. "A Bayesian semi-parametric model to estimate relationships between crash counts and roadway characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 699-715, June.
    4. Fabrizio Maturo & Rosanna Verde, 2023. "Supervised classification of curves via a combined use of functional data analysis and tree-based methods," Computational Statistics, Springer, vol. 38(1), pages 419-459, March.
    5. repec:jss:jstsof:18:i04 is not listed on IDEAS
    6. Boudaoud, S. & Rix, H. & Meste, O., 2010. "Core Shape modelling of a set of curves," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 308-325, February.
    7. Fabrizio Maturo & Antonio Balzanella & Tonio Di Battista, 2019. "Building Statistical Indicators of Equitable and Sustainable Well-Being in a Functional Framework," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(3), pages 449-471, December.
    8. C Rohrbeck & D A Costain & A Frigessi, 2018. "Bayesian spatial monotonic multiple regression," Biometrika, Biometrika Trust, vol. 105(3), pages 691-707.
    9. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    10. David BENATIA & Etienne BILLETTE de VILLEMEUR, 2019. "Strategic Reneging in Sequential Imperfect Markets," Working Papers 2019-19, Center for Research in Economics and Statistics.
    11. Cai, Bo & Dunson, David B., 2007. "Bayesian Multivariate Isotonic Regression Splines: Applications to Carcinogenicity Studies," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1158-1171, December.
    12. Mauricio Lopez-Mendez & Rowan Iskandar & Eric Jutkowitz, 2023. "Individual and Dyadic Health-Related Quality of Life of People Living with Dementia and their Caregivers," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 18(4), pages 1673-1692, August.
    13. Gabriel Riutort-Mayol & Virgilio Gómez-Rubio & José Luis Lerma & Julio M. del Hoyo-Meléndez, 2020. "Correlated Functional Models with Derivative Information for Modeling Microfading Spectrometry Data on Rock Art Paintings," Mathematics, MDPI, vol. 8(12), pages 1-25, December.
    14. Härdle, Wolfgang & Yatchew, Adonis, 2001. "Dynamic nonparametric state price density estimation using constrained least squares and the bootstrap," SFB 373 Discussion Papers 2002,16, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Ian Fillmore, 2021. "Price Discrimination and Public Policy in the U.S. College Market," Working Papers 2021-028, Human Capital and Economic Opportunity Working Group.
    16. Wu, Ximing & Sickles, Robin, 2018. "Semiparametric estimation under shape constraints," Econometrics and Statistics, Elsevier, vol. 6(C), pages 74-89.
    17. Björn Bornkamp & Katja Ickstadt, 2009. "Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose–Response Analysis," Biometrics, The International Biometric Society, vol. 65(1), pages 198-205, March.
    18. Michael Greenacre & Patrick J. F Groenen & Trevor Hastie & Alfonso Iodice d’Enza & Angelos Markos & Elena Tuzhilina, 2023. "Principal component analysis," Economics Working Papers 1856, Department of Economics and Business, Universitat Pompeu Fabra.
    19. John Haslett & Andrew Parnell, 2008. "A simple monotone process with application to radiocarbon‐dated depth chronologies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 399-418, September.
    20. Ng, Kenyon & Turlach, Berwin A. & Murray, Kevin, 2019. "A flexible sequential Monte Carlo algorithm for parametric constrained regression," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 13-26.
    21. Zhang, Ruizhi & Wang, Jian & Mei, Yajun, 2017. "Search for evergreens in science: A functional data analysis," Journal of Informetrics, Elsevier, vol. 11(3), pages 629-644.

    More about this item

    Statistics

    Access and download statistics

    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:wly:envmet:v:31:y:2020:i:8:n:e2645. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/1180-4009/ .

    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.