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Model averaging for global Fréchet regression

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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," LSE Research Online Documents on Economics 126533, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:126533
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    References listed on IDEAS

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    1. Danielle C. Tucker & Yichao Wu & Hans-Georg Müller, 2023. "Variable Selection for Global Fréchet Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1023-1037, April.
    2. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, September.
    3. Chao Ying & Zhou Yu, 2022. "Fréchet sufficient dimension reduction for random objects [Some asymptotic theory for the bootstrap]," Biometrika, Biometrika Trust, vol. 109(4), pages 975-992.
    4. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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