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Self‐modelling warping functions

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  • Daniel Gervini
  • Theo Gasser

Abstract

Summary. The paper introduces a semiparametric model for functional data. The warping functions are assumed to be linear combinations of q common components, which are estimated from the data (hence the name ‘self‐modelling’). Even small values of q provide remarkable model flexibility, comparable with nonparametric methods. At the same time, this approach avoids overfitting because the common components are estimated combining data across individuals. As a convenient by‐product, component scores are often interpretable and can be used for statistical inference (an example of classification based on scores is given).

Suggested Citation

  • Daniel Gervini & Theo Gasser, 2004. "Self‐modelling warping functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 959-971, November.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:4:p:959-971
    DOI: 10.1111/j.1467-9868.2004.B5582.x
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    References listed on IDEAS

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    1. Birgitte B. Rønn, 2001. "Nonparametric maximum likelihood estimation for shifted curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 243-259.
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    Cited by:

    1. Grith, Maria & Härdle, Wolfgang Karl & Park, Juhyun, 2009. "Shape invariant modelling pricing kernels and risk aversion," SFB 649 Discussion Papers 2009-041, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. Fang Yao & Yichao Wu & Jialin Zou, 2016. "Probability-enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-22, March.
    3. Tucker, J. Derek & Wu, Wei & Srivastava, Anuj, 2013. "Generative models for functional data using phase and amplitude separation," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 50-66.
    4. 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.
    5. Nikolaos Kampelis & Georgios I. Papayiannis & Dionysia Kolokotsa & Georgios N. Galanis & Daniela Isidori & Cristina Cristalli & Athanasios N. Yannacopoulos, 2020. "An Integrated Energy Simulation Model for Buildings," Energies, MDPI, vol. 13(5), pages 1-23, March.
    6. Dabo-Niang, Sophie & Guillas, Serge, 2010. "Functional semiparametric partially linear model with autoregressive errors," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 307-315, February.
    7. Arribas-Gil, Ana & Müller, Hans-Georg, 2014. "Pairwise dynamic time warping for event data," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 255-268.
    8. Fang Yao & Yichao Wu & Jialin Zou, 2016. "Probability-enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-22, March.
    9. Chu, Peter C. & Ivanov, Leonid M. & Margolina, Tetyana M., 2007. "On non-linear sensitivity of marine biological models to parameter variations," Ecological Modelling, Elsevier, vol. 206(3), pages 369-382.
    10. Gottlieb, Andrea & Müller, Hans-Georg, 2012. "A stickiness coefficient for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4000-4010.
    11. Jason Cleveland & Wei Wu & Anuj Srivastava, 2016. "Norm-preserving constraint in the Fisher--Rao registration and its application in signal estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 338-359, June.
    12. Cleveland, Jason & Zhao, Weilong & Wu, Wei, 2018. "Robust template estimation for functional data with phase variability using band depth," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 10-26.
    13. Daniel Gervini & Patrick A. Carter, 2014. "Warped functional analysis of variance," Biometrics, The International Biometric Society, vol. 70(3), pages 526-535, September.
    14. Ma, Yijia & Zhou, Xinyu & Wu, Wei, 2024. "A stochastic process representation for time warping functions," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    15. Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Vitelli, Valeria, 2010. "k-mean alignment for curve clustering," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1219-1233, May.
    16. Juhyun Park & Jeongyoun Ahn, 2017. "Clustering multivariate functional data with phase variation," Biometrics, The International Biometric Society, vol. 73(1), pages 324-333, March.
    17. Donatello Telesca & Lurdes Y.T. Inoue & Mauricio Neira & Ruth Etzioni & Martin Gleave & Colleen Nelson, 2009. "Differential Expression and Network Inferences through Functional Data Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 793-804, September.
    18. Gerda Claeskens & Bernard W. Silverman & Leen Slaets, 2010. "A multiresolution approach to time warping achieved by a Bayesian prior–posterior transfer fitting strategy," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 673-694, November.
    19. A. K. S. Alshabani & I. L. Dryden & C. D. Litton & J. Richardson, 2007. "Bayesian analysis of human movement curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 415-428, August.
    20. Zhang, Zhen & Müller, Hans-Georg, 2011. "Functional density synchronization," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2234-2249, July.
    21. Liu, Xueli & Yang, Mark C.K., 2009. "Simultaneous curve registration and clustering for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1361-1376, February.

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