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Pairwise dynamic time warping for event data

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  • Arribas-Gil, Ana
  • Müller, Hans-Georg

Abstract

A new version of dynamic time warping for samples of observed event times that are modeled as time-warped intensity processes is introduced. The approach is developed within a framework where for each experimental unit or subject in a sample, a random number of event times or random locations can be observed. As in this setting the number of observed events differs from subject to subject, usual landmark alignment methods that require the number of events to be the same across subjects are not feasible. This challenge is addressed by applying dynamic time warping, initially by aligning the event times for pairs of subjects, regardless of whether the numbers of observed events within the considered pair of subjects match. The information about pairwise alignments is then combined to extract an overall alignment of the events for each subject across the entire sample. This overall alignment provides a useful description of event data and can be used as a pre-processing step for subsequent analysis. The method is illustrated with a historical fertility study and with on-line auction data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:255-268
    DOI: 10.1016/j.csda.2013.08.011
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    References listed on IDEAS

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    1. Rong Tang & Hans-Georg Müller, 2008. "Pairwise curve synchronization for functional data," Biometrika, Biometrika Trust, vol. 95(4), pages 875-889.
    2. Kneip, Alois & Ramsay, James O, 2008. "Combining Registration and Fitting for Functional Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1155-1165.
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    4. 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.
    5. Xueli Liu & Hans-Georg Muller, 2004. "Functional Convex Averaging and Synchronization for Time-Warped Random Curves," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 687-699, January.
    6. Bouzas, P.R. & Valderrama, M.J. & Aguilera, A.M. & Ruiz-Fuentes, N., 2006. "Modelling the mean of a doubly stochastic Poisson process by functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2655-2667, June.
    7. Zhang, Zhen & Müller, Hans-Georg, 2011. "Functional density synchronization," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2234-2249, July.
    8. 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.
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    Cited by:

    1. Arribas-Gil Ana & Matias Catherine, 2017. "A time warping approach to multiple sequence alignment," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(2), pages 133-144, April.
    2. Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    3. Irene Albarrán-Lozano & Pablo J. Alonso-González & Ana Arribas-Gil, 2017. "Dependence evolution in the Spanish disabled population: a functional data analysis approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 657-677, February.
    4. Aleksandra Rutkowska & Magdalena Szyszko, 2022. "New DTW Windows Type for Forward- and Backward-Lookingness Examination. Application for Inflation Expectation," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 701-718, February.

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