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Estimation and model selection for nonparametric function-on-function regression.

Zhanfeng Wang1, Hao Dong2, Ping Ma3

  • 1International Institute of Finance, The School of Management, University of Science and Technology of China.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|January 3, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for nonparametric function-on-function regression, enhancing model selection and diagnostics using smoothing spline analysis of variance (SS ANOVA) and L1 penalty. The methods offer powerful tools for analyzing complex functional data.

Keywords:
Convergence rateRegularizationReproducing kernel Hilbert spaceSmoothing spline ANOVA

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Nonparametric Regression

Background:

  • Functional regression models are increasingly important but lack robust model selection and diagnostic tools.
  • Existing nonparametric and semiparametric methods do not fully address the need for unified frameworks.

Purpose of the Study:

  • To develop a unified framework for estimation and model selection in nonparametric function-on-function regression.
  • To introduce powerful tools for model selection and diagnostics in functional regression.

Main Methods:

  • Proposed a general nonparametric functional regression model using smoothing spline analysis of variance (SS ANOVA) decomposition.
  • Developed new estimation procedures utilizing L1 and L2 penalties.
  • Investigated the combination of SS ANOVA decomposition and L1 penalty for enhanced model selection and diagnostics.

Main Results:

  • Established consistency and convergence rates for estimates of the regression function and its components under both L1 and L2 penalties.
  • Demonstrated that the SS ANOVA decomposition with an L1 penalty effectively aids in model selection and diagnostics.
  • Simulation studies and real-world examples confirmed the efficacy of the proposed methods.

Conclusions:

  • The proposed unified framework provides effective tools for nonparametric function-on-function regression.
  • The combination of SS ANOVA and L1 penalty offers a powerful approach for model selection and diagnostics in functional data analysis.