2021/08/12 by Alexander Bauer, Fabian Scheipl, Bauer, Alexander +6
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference #stat.ME
paper · pdf · doi:10.48550/arxiv.2108.05634
Excluding the Appendix (i.e. the second half of the submitted pdf): 41 pages, 8 figures Including the Appendix: 74 pages, 32 figures Submitted to Journal of Computational and Graphical Statistics
arxiv created 2021/08/12 · openalex publication_date 2021/08/12 · arxiv updated 2021/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Accounting for phase variability is a critical challenge in functional data analysis. To separate it from amplitude variation, functional data are registered, i.e., their observed domains are deformed elastically so that the resulting functions are aligned with template functions. At present, most available registration approaches are limited to datasets of complete and densely measured curves with Gaussian noise. However, many real-world functional data sets are not Gaussian and contain incomplete curves, in which the underlying process is not recorded over its entire domain. In this work, we extend and refine a framework for joint likelihood-based registration and latent Gaussian process-based generalized functional principal component analysis that is able to handle incomplete curves. Our approach is accompanied by sophisticated open-source software, allowing for its application in diverse non-Gaussian data settings and a public code repository to reproduce all results. We register data from a seismological application comprising spatially indexed, incomplete ground velocity time series with a highly volatile Gamma structure. We describe, implement and evaluate the approach for such incomplete non-Gaussian functional data and compare it to existing routines.