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Simultaneous inference for misaligned multivariate functional data
- Publication Year :
- 2016
-
Abstract
- 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.<br />Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and references
- Subjects :
- Statistics - Applications
62H99
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1606.03295
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1111/rssc.12276