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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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ESTIMATION AND VARIABLE SELECTION FOR GENERALIZED ADDITIVE PARTIAL LINEAR MODELS.

Li Wang1, Xiang Liu, Hua Liang

  • 1Department of Statistics, University of Georgia, Athens, Georgia 30602, USA, lilywang@uga.edu.

Annals of Statistics
|December 18, 2012
PubMed
Summary

This study introduces polynomial spline smoothing for generalized additive partial linear models, offering computational simplicity and effective variable selection for linear parameters. The new method demonstrates an asymptotic oracle property for improved statistical estimation.

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Econometrics

Background:

  • Generalized additive partial linear models (GAPLMs) are complex statistical tools.
  • Existing estimation methods, like kernel-based procedures, can be computationally intensive.
  • Efficient variable selection within these models remains a challenge.

Purpose of the Study:

  • To propose a computationally simpler estimation method for GAPLMs using polynomial spline smoothing.
  • To develop and validate a variable selection procedure for the linear components of GAPLMs.
  • To establish the theoretical properties of the proposed estimators.

Main Methods:

  • Utilizing polynomial spline smoothing for estimating nonparametric functions within GAPLMs.
  • Deriving quasi-likelihood based estimators for the linear parameters.
  • Employing a nonconcave penalized quasi-likelihood for variable selection.

Main Results:

  • Asymptotic normality is established for the estimators of the parametric components.
  • The proposed method offers significant computational advantages over kernel-based approaches.
  • The variable selection procedure demonstrates an asymptotic oracle property.

Conclusions:

  • Polynomial spline smoothing provides an efficient and computationally simple approach for GAPLMs.
  • The developed variable selection technique enhances model interpretability and performance.
  • The findings offer a practical advancement for statistical modeling and analysis.