Nonparametric and Robust Inference for Covariance Operators
Kelly Ramsay, PhD
Assistant Professor | Department of Mathematics and Statistics
York University
WHEN: Wednesday, February 7, 2024, from 3:30 to 4:30 p.m.
WHERE: hybrid | 2001 McGill College Avenue, room 1140;
NOTE: Dr. Ramsay will be presenting from Toronto
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Abstract
Conducting inference for functional data has various challenges. Some of these challenges include a lack of parametric models, slow computation, high-dimensionality, and outliers. We can overcome many of these issues, in the context of multi-sample testing for differences in the covariance operator, using functional Kruskal-Wallis for covariance (FKWC) rank tests. FKWC rank tests use a pooled center-outward ordering of the sampled functions to measure differences in covariance structure between samples. The ordering is based on functional data depth, which we show is connected to the covariance operator. Various aspects of these tests are discussed, along with an application to phoneme data. A related problem is multiple change-point detection in the covariance structure of functional and multivariate data. We present FKWC procedures in the context of change-point detection, with an application to resting state f-MRI data.
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