  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.
