A0360
Title: Transportation-based change point detection and testing for functional covariances
Authors: Valentina Masarotto - Leiden University (Netherlands) [presenting]
Abstract: The analysis of variation within a sample of stochastic processes is addressed, particularly focusing on their second-order covariance structure. Covariance operators are primarily known in functional data analysis for the crucial role they play in the Karhunen-Love expansion. However, these operators themselves may exhibit variability and necessitate statistical techniques tailored to assess their fluctuations. Such techniques are closely tied to the choice of metric on covariance operators and, if mastered, grant access to powerful statistical procedures. The geometric properties of the space of functional covariances are leveraged to develop inferential tools for such operators. In particular, by identifying covariances with centered Gaussian processes, results from optimal transport theory are exploited, in addition to functional data analysis. A novel approach is introduced to k-sample testing in the functional setting, which, in turn, will be applied to the detection of structural breaks in the covariance of a sample of functional data. By navigating the complex relationship between geometry, statistical theory, and functional analysis, the aim is to provide a systematic framework for nuanced inference and robust detection within the realm of stochastic processes. All algorithms presented are illustrated using real data and are implemented in the R package fdWasserstein.
