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Simultaneous inference for misaligned multivariate functional data
We consider inference for misaligned multivariate functional data that
represents the same underlying curve, but where the functional samples have
systematic differences in shape. In this paper we introduce a new class of
generally applicable models where warping effects are modeled through nonlinear
transformation of latent Gaussian variables and systematic shape differences
are modeled by Gaussian processes. To model cross-covariance between sample
coordinates we introduce a class of low-dimensional cross-covariance structures
suitable for modeling multivariate functional data. We present a method for
doing maximum-likelihood estimation in the models and apply the method to three
data sets. The first data set is from a motion tracking system where the
spatial positions of a large number of body-markers are tracked in
three-dimensions over time. The second data set consists of height and weight
measurements for Danish boys. The third data set consists of three-dimensional
spatial hand paths from a controlled obstacle-avoidance experiment. We use the
developed method to estimate the cross-covariance structure, and use a
classification setup to demonstrate that the method outperforms
state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of
supplementary material and reference
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