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Title: Functional models for time-varying random objects Authors:  Paromita Dubey - Stanford University (United States)
Hans-Georg Mueller - University of California Davis (United States) [presenting]
Abstract: In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have become increasingly prevalent. Such data are elements of a general metric space that lacks local or global linear structure. Common approaches that have been used with great success for the analysis of functional data, such as functional principal component analysis, are therefore not applicable. The concept of metric covariance makes it possible to define a metric auto-covariance function for a sample of random curves that take values in a general metric space. This metric auto-covariance function is non-negative definite when the squared semi-metric of the underlying space is of negative type. Then the eigenfunctions of the linear operator with the auto-covariance function as kernel can be used as building blocks for an object functional principal component analysis, which includes real-valued Frechet scores and metric-space valued object functional principal components. Sample-based estimates of these quantities are shown to be asymptotically consistent and are illustrated with time-varying networks and other data.