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Smooth and Locally Sparse Estimation for Multiple-Output Functional Linear Regression.

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|October 5, 2020
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Summary
This summary is machine-generated.

We introduce a new method for functional linear regression that achieves functional sparsity by identifying and zeroing out irrelevant predictor-response relationships. This approach enhances estimation accuracy for coefficient functions, particularly in multivariate settings.

Keywords:
Functional data analysisfunctional linear multivariate regressionlocally sparse

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Functional data analysis seeks sparse estimates, setting coefficients to zero where no relationship exists.
  • Existing methods may not fully leverage interconnections among multiple response variables.

Purpose of the Study:

  • To propose a novel estimator for coefficient functions in functional linear regression models.
  • To incorporate interconnections among responses for improved functional sparsity.

Main Methods:

  • Developed the multiple-smooth and locally sparse (m-SLoS) estimator.
  • Combined smooth and locally sparse (SLoS) estimation with a Laplacian quadratic penalty.
  • Utilized SLoS for local sparsity and Laplacian penalty for similarity across coefficient functions.

Main Results:

  • The m-SLoS estimator demonstrated excellent numerical performance in simulations.
  • Accurate estimation of coefficient functions was achieved, especially when functions were identical across multivariate responses.
  • The method showed significant prediction improvements in a real-world application.

Conclusions:

  • The proposed m-SLoS method effectively achieves functional sparsity in regression models.
  • Leveraging response interconnections enhances the estimation of coefficient functions.
  • The approach offers practical benefits and improved predictive power.