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Rank dynamics for functional data

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  • 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
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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Samanta, M., 1989. "Non-parametric estimation of conditional quantiles," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 407-412, April.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    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.
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