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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

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Published on: July 3, 2020

Structured penalties for functional linear models-partially empirical eigenvectors for regression.

Timothy W Randolph1, Jaroslaw Harezlak, Ziding Feng

  • 1Fred Hutchinson Cancer Research Center, Biostatistics and Biomathematics Program, Seattle, WA 98109.

Electronic Journal of Statistics
|May 29, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a unified approach for analyzing functional data with geometric structure, enhancing functional linear models. The method uses generalized singular value decomposition (GSVD) for improved estimation of coefficient functions in biomedical data analysis.

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Last Updated: May 22, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Statistical analysis
  • Biomedical data science
  • Functional data analysis

Background:

  • Incorporating geometric structure (local correlation) into functional data analysis is challenging.
  • Functional linear models are common for relating predictor functions to scalar responses in biomedical technologies.
  • Existing methods often use two-stage regularization via dimension reduction (basis functions or principal components).

Purpose of the Study:

  • To present a unified approach for functional data analysis that directly incorporates geometric structure.
  • To improve the estimation of coefficient functions in functional linear models.
  • To clarify the role of penalty operators and predictors in bias-variance trade-offs.

Main Methods:

  • Exploiting joint eigenproperties of predictors and a linear penalty operator.
  • Utilizing the generalized singular value decomposition (GSVD) framework.
  • Developing a penalized estimation approach informed by GSVD.

Main Results:

  • The GSVD framework provides a unified approach to penalized estimation.
  • The method explicitly reveals the joint influence of penalty and predictors on estimation performance.
  • Demonstrated utility with laboratory spectroscopy data and simulations.

Conclusions:

  • The proposed GSVD-based method offers a clearer understanding and improved estimation for functional data with geometric structure.
  • This approach enhances the analysis of complex biomedical data.
  • The framework guides penalty selection for optimal bias-variance balance.