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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.
Biometrics
|May 7, 2025
Summary
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.
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.
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