IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v58y2009i2p267-284.html
   My bibliography  Save this article

A functional approach to diversity profiles

Author

Listed:
  • Stefano A. Gattone
  • Tonio Di Battista

Abstract

Summary. Diversity plays a central role in ecological theory and its conservation and management are important issues for the wellbeing and stability of ecosystems. The aim of this work is to provide a reliable theoretical framework for performing statistical analysis on ecological diversity by means of the joint use of diversity profiles and functional data analysis. We point out that ecological diversity is a multivariate concept as it is a function of the relative abundances of species in a biological community. For this, several researchers have suggested using parametric families of indices of diversity for obtaining more information from the data. Patil and Taillie introduced the concept of intrinsic diversity ordering which can be determined by using the diversity profile. It may be noted that the diversity profile is a non‐negative and convex curve which consists of a sequence of measurements as a function of a given parameter. Thus, diversity profiles can be explained through a process that is described in a functional setting. Recent developments in environmental studies have focused on the opportunity to evaluate community diversity changes over space and/or correlation of diversity with environmental characteristics. For this, we develop an innovative analysis of diversity based on a functional data approach. Whereas conventional statistical methods process data as a sequence of individual observations, functional data analysis is designed to process a collection of functions or curves. Moreover, unconstrained models may lead to negative and/or non‐convex estimates for the diversity profiles. To overcome this problem, a transformation is proposed which can be constrained to be non‐negative and convex. We focus on some applications showing how functional data analysis provides an alternative way of understanding biological diversity and its interaction with natural and/or human factors.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:58:y:2009:i:2:p:267-284
    DOI: 10.1111/j.1467-9876.2009.00646.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9876.2009.00646.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9876.2009.00646.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
    ---><---

    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. Dole, David, 1999. "CoSmo: A Constrained Scatterplot Smoother for Estimating Convex, Monotonic Transformations," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(4), pages 444-455, October.
    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. 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. Fabrizio Maturo & Stefania Migliori & Francesco Paolone, 2019. "Measuring and monitoring diversity in organizations through functional instruments with an application to ethnic workforce diversity of the U.S. Federal Agencies," Computational and Mathematical Organization Theory, Springer, vol. 25(4), pages 357-388, December.
    3. Francesca Fortuna & Stefano Antonio Gattone & Tonio Di Battista, 2020. "Functional estimation of diversity profiles," Environmetrics, John Wiley & Sons, Ltd., vol. 31(8), December.
    4. 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.

    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. Wu, Ximing & Sickles, Robin, 2018. "Semiparametric estimation under shape constraints," Econometrics and Statistics, Elsevier, vol. 6(C), pages 74-89.
    2. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    3. Davies, P. Laurie & Kovac, A., 1999. "Modality, runs, strings and wavelets," Technical Reports 1999,16, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. 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.
    5. Debashis Ghosh & Moulinath Banerjee & Pinaki Biswas, 2008. "Inference for Constrained Estimation of Tumor Size Distributions," Biometrics, The International Biometric Society, vol. 64(4), pages 1009-1017, December.
    6. Zhang, Yu Yvette, 2017. "A shape constrained estimator of bidding function of first-price sealed-bid auctions," Economics Letters, Elsevier, vol. 150(C), pages 67-72.
    7. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    8. Wenchuan Liu & Yu Zhang & Qi Li, 2015. "A semiparametric varying coefficient model of monotone auction bidding processes," Empirical Economics, Springer, vol. 48(1), pages 313-335, February.
    9. 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.
    10. Birke, Melanie & Dette, Holger, 2006. "Testing strict monotonicity in nonparametric regression," Technical Reports 2006,49, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    11. 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.
    12. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    13. Wei Wang & Dylan S. Small, 2015. "Monotone B-Spline Smoothing for a Generalized Linear Model Response," The American Statistician, Taylor & Francis Journals, vol. 69(1), pages 28-33, February.
    14. 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.
    15. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    16. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    17. Kevin Murray & Samuel Müller & Berwin Turlach, 2013. "Revisiting fitting monotone polynomials to data," Computational Statistics, Springer, vol. 28(5), pages 1989-2005, October.
    18. Golchi, Shirin & Campbell, David A., 2016. "Sequentially Constrained Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 98-113.
    19. Benatia, David & Billette de Villemeur, Etienne, 2019. "Strategic Reneging in Sequential Imperfect Markets," MPRA Paper 105280, University Library of Munich, Germany, revised Jan 2020.
    20. 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.

    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:bla:jorssc:v:58:y:2009:i:2:p:267-284. 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: https://edirc.repec.org/data/rssssea.html .

    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.