Abstract

By defining a logarithmic functional central subspace along the Fr´echet mean curve, a novel

intrinsic functional sliced inverse regression model is proposed for a Riemannian or Wasserstein functional predictor and a scalar response. This approach is applicable to both Euclidean submanifolds

and manifolds without a natural ambient space. Under mild conditions, a truncation-based estimation

procedure is developed for the logarithmic functional central subspace, and its asymptotic properties

are subsequently investigated within the framework of intrinsic geometry. Furthermore, the flatness of

the Wasserstein space ensures that the proposed method can identify the optimal truncation number

to achieve the minimax optimal convergence rate for estimating the logarithmic functional central subspace. The finite-sample performance of the proposed method is demonstrated through both simulation

studies and real data applications.

Information

Preprint No.SS-2024-0349
Manuscript IDSS-2024-0349
Complete AuthorsXinyu Li, Jianjun Xu
Corresponding AuthorsJianjun Xu
Emailsxjj1994@mail.ustc.edu.cn

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Acknowledgments

We thank the Co-Editor, an associate editor and two anonymous referees for their helpful

comments and constructive suggestions. This research was supported by the Fundamental

Research Funds for the Central Universities [Grant number JZ2024HGQA0121, JZ2025HGTA0142]

and the China Postdoctoral Science Foundation [Grant number 2023M733406].

Supplementary Materials

The supplementary material contains the proofs of theoretical results and additional numerical results.

Supplementary materials are available for download.