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Abstract:
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Faced with new types of data, statisticians require suitable models and methods to work with samples of complex random objects. We consider random objects that lie in a metric space such as distributions, covariance matrices and networks. When exploring the interface between functional data analysis and random objects, a major challenge is the lack of basic algebraic operations in the metric space where the random objects live. We will discuss how to harness the novel tools of Frechet regression and Frechet integration to address this challenge. Frechet regression is based on an extension of the notion of Frechet means to conditional Frechet means and leads to useful regression models in general metric spaces, while Frechet integration can be employed to define projections for time-varying random objects. The proposed methods are supported by empirical process theory and will be demonstrated for various data applications. This presentation is based on joint work with Alexander Petersen and Paromita Dubey.
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