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Fr\'echet Means in Infinite Dimensions

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arxiv 2410.17214 v3 pith:ZZY3VEKJ submitted 2024-10-22 math.PR math.FAmath.MG

Adam Quinn Jaffe This is my paper · ORCID
classification math.PRmath.FAmath.MG
keywords metricechetmeansasymptoticgeneralinfinite-dimensionalresultsspaces
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While there exists a well-developed asymptotic theory of Fr\'echet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known results in which the random variables can take values in an "infinite-dimensional" metric space. Presently, we develop a general asymptotic theory of Fr\'echet means in some infinite-dimensional metric spaces, which allows us to recover, strengthen, and generalize most existing results; in particular, we develop novel asymptotic theory for Fr\'echet means in some infinite-dimensional metric spaces from statistical shape analysis. The core of the proof is a novel notion of weak convergence in general metric spaces for which the results can be proven via calculus of variations.

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Cited by 3 Pith papers

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