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Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
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Distance weighted directional regression for Fréchet sufficient dimension reduction.

Chao Ying1, Zhou Yu2, Xin Zhang3

  • 1Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI 53705, United States.

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|May 7, 2025
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Summary
This summary is machine-generated.

This study introduces distance weighted directional regression for analyzing complex non-Euclidean data. The method unifies sufficient dimension reduction for various data types, improving prediction and interpretation in longevity and health studies.

Keywords:
Fréchet regressiondirectional regressioninverse regressionsufficient dimension reduction

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Area of Science:

  • Statistics
  • Data Science
  • Dimensionality Reduction

Background:

  • Analysis of non-Euclidean data is crucial in fields like human longevity and brain network studies.
  • Fréchet sufficient dimension reduction (FSDR) seeks to uncover relationships between complex object-valued responses and predictors, while reducing predictor dimensionality.

Purpose of the Study:

  • To introduce a unified distance weighted directional regression method for both linear and nonlinear Fréchet sufficient dimension reduction.
  • To extend the classical directional regression framework for handling non-Euclidean data.

Main Methods:

  • Developed a novel distance weighting approach for directional regression.
  • Formulated a unified method applicable to both Euclidean and non-Euclidean responses.
  • Extended the method to nonlinear FSDR.

Main Results:

  • Derived the asymptotic normality for the linear FSDR estimator.
  • Established the convergence rate for the nonlinear FSDR estimator.
  • Simulation studies confirmed the empirical performance and theoretical findings.

Conclusions:

  • The proposed distance weighted directional regression offers a unified approach for FSDR.
  • The method enhances interpretation and out-of-sample prediction, as demonstrated in human mortality and diabetes prevalence analyses.