Model averaging for global Fréchet regression

Daisuke Kurisu and Taisuke Otsu

Journal of Multivariate Analysis, 2025, vol. 207, issue C

Abstract: Non-Euclidean complex data analysis becomes increasingly popular in various fields of data science. In a seminal paper, Petersen and Müller (2019) generalized the notion of regression analysis to non-Euclidean response objects. Meanwhile, in the conventional regression analysis, model averaging has a long history and is widely applied in statistics literature. This paper studies the problem of optimal prediction for non-Euclidean objects by extending the method of model averaging. In particular, we generalize the notion of model averaging for global Fréchet regressions and establish an optimal property of the cross-validation to select the averaging weights in terms of the final prediction error. A simulation study illustrates excellent out-of-sample predictions of the proposed method.

Keywords: Asymptotic optimality; Cross-validation; Global Fréchet regression; Model averaging (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.jmva.2025.105416

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