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Model averaging for global Fréchet regression

Author

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  • Kurisu, Daisuke
  • Otsu, Taisuke

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.

Suggested Citation

  • Kurisu, Daisuke & Otsu, Taisuke, 2025. "Model averaging for global Fréchet regression," Journal of Multivariate Analysis, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:jmvana:v:207:y:2025:i:c:s0047259x25000119
    DOI: 10.1016/j.jmva.2025.105416
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