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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Functional Mixed Effects Model for Small Area Estimation.

Tapabrata Maiti1, Samiran Sinha2, Ping-Shou Zhong1

  • 1Department of Statistics & Probability, Michigan State University, East Lansing, MI 48824.

Scandinavian Journal of Statistics, Theory and Applications
|November 1, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a new varying coefficient linear mixed model for small area estimation, improving functional data analysis. The method offers accurate parameter estimation and uncertainty measurement for complex datasets.

Keywords:
B-splinesBest linear unbiased predictorFunctional data analysisLinear mixed modelsMean squared errorRestricted maximum likelihoodSmall area estimationVariance components

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Functional data analysis (FDA) is crucial for high-dimensional data.
  • Linear mixed-effect models (LMEMs) are fundamental to small area estimation (SAE).
  • Existing FDA methods have limitations within LMEMs for SAE.

Purpose of the Study:

  • To develop a novel varying coefficient LMEM for area-level data in SAE.
  • To address limitations in current FDA approaches for SAE.
  • To provide a practical method for parameter estimation and prediction uncertainty.

Main Methods:

  • Fitting a varying coefficient LMEM with semi-parametric B-spline modeling.
  • Developing methods for fixed effect parameter estimation.
  • Proposing a prediction method for random effects implementable in standard software.
  • Deriving analytical expressions and methods for mean squared error estimation.

Main Results:

  • The proposed method effectively estimates parameters and predicts random effects.
  • Analytical expressions for mean squared errors (MSEs) were derived.
  • A practical MSE estimation procedure was developed.
  • Simulation studies validated the method's operating characteristics.

Conclusions:

  • The developed varying coefficient LMEM offers a robust approach for FDA in SAE.
  • The method provides reliable estimation and uncertainty quantification.
  • The approach is practical and validated through real data and simulations.