ArticleAnnals of statistics2025
NONLINEAR GLOBAL FRÉCHET REGRESSION FOR RANDOM OBJECTS VIA WEAK CONDITIONAL EXPECTATION.
Article in Annals of statistics, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
3 citing papers in PubMed.
- FAST VARIABLE SELECTION FOR DISTRIBUTIONAL REGRESSION WITH APPLICATION TO CONTINUOUS GLUCOSE MONITORING DATA.The annals of applied statistics · 2025Article
- NONLINEAR GLOBAL FRÉCHET REGRESSION FOR RANDOM OBJECTS VIA WEAK CONDITIONAL EXPECTATION.Annals of statistics · 2025Article
- Nonlinear sufficient dimension reduction for distribution-on-distribution regression.Journal of multivariate analysis · 2024Article
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Authors and funding
3 authors.
Funding
Abstract
Random objects are complex non-Euclidean data taking values in general metric spaces, possibly devoid of any underlying vector space structure. Such data are becoming increasingly abundant with the rapid advancement in technology. Examples include probability distributions, positive semidefinite matrices and data on Riemannian manifolds. However, except for regression for object-valued response with Euclidean predictors and distribution-on-distribution regression, there has been limited development of a general framework for object-valued response with object-valued predictors in the literature. To fill this gap, we introduce the notion of a weak conditional Fréchet mean based on Carleman operators and then propose a global nonlinear Fréchet regression model through the reproducing kernel Hilbert space (RKHS) embedding. Furthermore, we establish the relationships between the conditional Fréchet mean and the weak conditional Fréchet mean for both Euclidean and object-valued data. We also show that the state-of-the-art global Fréchet regression developed by Petersen and Müller (
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