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A multiresolution approach to time warping achieved by a Bayesian prior–posterior transfer fitting strategy

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  • Gerda Claeskens
  • Bernard W. Silverman
  • Leen Slaets

Abstract

Summary. Warping is an approach to the reduction and analysis of phase variability in functional observations, by applying a smooth bijection to the function argument. We propose a natural representation of warping functions in terms of a new type of elementary functions named ‘warping component functions’, or ‘warplets’, which are combined into the warping function by composition. The inverse warping function is trivial and explicit to obtain. A sequential Bayesian estimation strategy is introduced which fits a series of models and transfers the posterior of the previous fit into the prior of the next fit. Model selection is based on a warping analogue to wavelet thresholding, combined with Bayesian inference.

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  • 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.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:5:p:673-694
    DOI: 10.1111/j.1467-9868.2010.00752.x
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Slaets, Leen & Claeskens, Gerda & Silverman, Bernard W., 2013. "Warping Functional Data in R and C via a Bayesian Multiresolution Approach," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i03).
    2. Daniel Gervini & Patrick A. Carter, 2014. "Warped functional analysis of variance," Biometrics, The International Biometric Society, vol. 70(3), pages 526-535, September.
    3. Slaets, Leen & Claeskens, Gerda & Hubert, Mia, 2012. "Phase and amplitude-based clustering for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2360-2374.
    4. Wagner, Heiko & Kneip, Alois, 2019. "Nonparametric registration to low-dimensional function spaces," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 49-63.

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