IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v149y2020ics0167947320300542.html
   My bibliography  Save this article

Rank dynamics for functional data

Author

Listed:
  • Chen, Yaqing
  • Dawson, Matthew
  • Müller, Hans-Georg

Abstract

The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional data. This approach is of interest in various application areas. For the analysis of the dynamics of ranks, estimation of the cross-sectional ranks of functional data is a first step. Several statistics of interest for ranked functional data are proposed. To quantify the evolution of ranks over time, a model for rank derivatives is introduced, where rank dynamics are decomposed into two components. One component corresponds to population changes and the other to individual changes that both affect the rank trajectories of individuals. The joint asymptotic normality for suitable estimates of these two components is established. The proposed approaches are illustrated with simulations and three longitudinal datasets: Growth curves obtained from the Zürich Longitudinal Growth Study, monthly house price data in the US from 1996 to 2015 and Major League Baseball offensive data for the 2017 season.

Suggested Citation

  • Chen, Yaqing & Dawson, Matthew & Müller, Hans-Georg, 2020. "Rank dynamics for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    • Handle: RePEc:eee:csdana:v:149:y:2020:i:c:s0167947320300542
    DOI: 10.1016/j.csda.2020.106963
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947320300542
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2020.106963?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. Tao Chen & Qingliang Fan, 2018. "A functional data approach to model score difference process in professional basketball games," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 112-127, January.
    2. Ximing Wu & Jeffrey M. Perloff, 2005. "China's Income Distribution, 1985-2001," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 763-775, November.
    3. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    4. B. Martin-Barragan & R.E. Lillo & J. Romo, 2016. "Functional boxplots based on epigraphs and hypographs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(6), pages 1088-1103, May.
    5. Muller, Hans-Georg & Stadtmuller, Ulrich & Yao, Fang, 2006. "Functional Variance Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1007-1018, September.
    6. Colin O. Wu & Xin Tian, 2013. "Nonparametric Estimation of Conditional Distributions and Rank-Tracking Probabilities With Time-Varying Transformation Models in Longitudinal Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 971-982, September.
    7. Richard Barnett & Joydeep Bhattacharya & Helle Bunzel, 2010. "Choosing to keep up with the Joneses and income inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(3), pages 469-496, December.
    8. 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.
    9. Belalia, Mohamed & Bouezmarni, Taoufik & Leblanc, Alexandre, 2017. "Smooth conditional distribution estimators using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 166-182.
    10. Noël Veraverbeke & Irène Gijbels & Marek Omelka, 2014. "Preadjusted non-parametric estimation of a conditional distribution function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 399-438, March.
    11. Ramsay, James O. & Ramsey, James B., 2002. "Functional data analysis of the dynamics of the monthly index of nondurable goods production," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 327-344, March.
    12. Samanta, M., 1989. "Non-parametric estimation of conditional quantiles," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 407-412, April.
    13. Wang, Shanshan & Jank, Wolfgang & Shmueli, Galit, 2008. "Explaining and Forecasting Online Auction Prices and Their Dynamics Using Functional Data Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 144-160, April.
    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. Claus Thorn Ekstrøm & Andreas Kryger Jensen, 2023. "Having a ball: evaluating scoring streaks and game excitement using in-match trend estimation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 295-311, March.

    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 Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    2. Eppelsheimer, Johann & Rust, Christoph, 2020. "The Spatial Decay of Human Capital Externalities - A Functional Regression Approach with Precise Geo-Referenced Data," IAB-Discussion Paper 202021, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    3. Matthias Hansmann & Benjamin M. Horn & Michael Kohler & Stefan Ulbrich, 2022. "Estimation of conditional distribution functions from data with additional errors applied to shape optimization," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 323-343, April.
    4. Eppelsheimer, Johann & Jahn, Elke J. & Rust, Christoph, 2022. "The spatial decay of human capital externalities - A functional regression approach with precise geo-referenced data," Regional Science and Urban Economics, Elsevier, vol. 95(C).
    5. Zongwu Cai & Xian Wang, 2013. "Nonparametric Methods for Estimating Conditional VaR and Expected Shortfall," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Ioannides, D. A., 2004. "Fixed design regression quantiles for time series," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 235-245, July.
    7. Belalia, Mohamed & Bouezmarni, Taoufik & Leblanc, Alexandre, 2017. "Smooth conditional distribution estimators using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 166-182.
    8. Genest Christian & Scherer Matthias, 2023. "When copulas and smoothing met: An interview with Irène Gijbels," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-16, January.
    9. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    10. Chen Shi & Yujiao Xian & Zhixin Wang & Ke Wang, 2023. "Marginal abatement cost curve of carbon emissions in China: a functional data analysis," Mitigation and Adaptation Strategies for Global Change, Springer, vol. 28(2), pages 1-25, February.
    11. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    12. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    13. Qianwen Tan & Subhashis Ghosal, 2021. "Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 3-29, May.
    14. Qu, Zhaopeng (Frank) & Zhao, Zhong, 2008. "Urban-Rural Consumption Inequality in China from 1988 to 2002: Evidence from Quantile Regression Decomposition," IZA Discussion Papers 3659, Institute of Labor Economics (IZA).
    15. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    16. Jaeger, Jonathan & Lambert, Philippe, 2012. "Bayesian penalized smoothing approaches in models specified using affine differential equations with unknown error distributions," LIDAM Discussion Papers ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Cao, Jiguo & Ramsay, James O., 2009. "Generalized profiling estimation for global and adaptive penalized spline smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2550-2562, May.
    18. Hooker, Giles & Ramsay, James O. & Xiao, Luo, 2016. "CollocInfer: Collocation Inference in Differential Equation Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 75(i02).
    19. Siphumlile Mangisa & Sonali Das & Rangan Gupta, 2022. "Analyzing The Impact Of Brexit On Global Uncertainty Using Functional Linear Regression With Point Of Impact: The Role Of Currency And Equity Markets," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 67(04), pages 1377-1388, June.
    20. Martins-Filho, Carlos & Ziegelmann, Flávio Augusto & Torrent, Hudson da Silva, 2013. "Local Exponential Frontier Estimation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 33(2), November.
    21. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.

    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:149:y:2020:i:c:s0167947320300542. 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.