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• W3037281036 abstract "Local Fréchet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy metric space valued random objects. We derive uniform rates of convergence, which so far have eluded theoretical analysis of this method, for both fixed and random target trajectories, where we utilize tools from empirical processes. These results are shown to be widely applicable in metric space valued data analysis. In addition to simulations, we provide two pertinent examples where these results are important: The consistent estimation of the location of properly defined extrema in metric space valued trajectories, which we illustrate with the problem of locating the age of minimum brain connectivity as obtained from fMRI data; and time warping for metric space valued trajectories, illustrated with yearly age-at-death distributions for different countries." @default.
• W3037281036 created "2020-07-02" @default.
• W3037281036 creator A5050634491 @default.
• W3037281036 creator A5060071396 @default.
• W3037281036 date "2022-06-01" @default.
• W3037281036 modified "2023-10-16" @default.
• W3037281036 title "Uniform convergence of local Fréchet regression with applications to locating extrema and time warping for metric space valued trajectories" @default.
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• W3037281036 doi "https://doi.org/10.1214/21-aos2163" @default.
• W3037281036 hasPublicationYear "2022" @default.
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