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Detection of Interaction Effects in a Nonparametric Concurrent Regression Model.

Rui Pan1, Zhanfeng Wang2, Yaohua Wu2

  • 1School of Data Science, University of Science and Technology of China, Hefei 230026, China.

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|September 28, 2023
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Summary

This study introduces a new model selection method for functional data analysis, enabling the detection of interaction effects in complex functional regression models. The approach is validated using simulations and real-world stroke rehabilitation data.

Keywords:
L1 criterionmodel selectionreproducing kernel Hilbert spacesmoothing spline

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Machine Learning

Background:

  • Nonparametric function-on-function regression models are crucial for analyzing complex data.
  • Existing methods lack robust model selection for functional regression with functional covariates.
  • Understanding interaction effects among functional covariates is essential.

Purpose of the Study:

  • To develop a novel model selection approach for function-on-function regression with functional covariates.
  • To identify and analyze interaction effects within functional covariate inputs.
  • To provide a method for estimating the functional regression function in this context.

Main Methods:

  • Constructed a tensor product space of reproducing kernel Hilbert spaces.
  • Developed an analysis of variance (ANOVA) decomposition for the tensor product space.
  • Employed an L1 criterion-based model selection method for estimation and interaction detection.

Main Results:

  • Successfully estimated the functional regression function with functional covariate inputs.
  • Demonstrated the ability to detect interaction effects among functional covariates.
  • Validated the proposed method through comprehensive simulations.

Conclusions:

  • The proposed L1-based model selection method effectively addresses the challenge of analyzing interaction effects in nonparametric function-on-function regression.
  • The method shows promise for applications in fields like medical research, as evidenced by its evaluation on stroke rehabilitation data.