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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

Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models.

Hua Liang1, Hulin Wu

  • 1Hua Liang (E-mail: hliang@bst.rochester.edu ) is Associate Professor and Hulin Wu ( hwu@bst.rochester.edu ) is Professor, Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, 601 Elmwood Avenue, Box 630, Rochester, New York 14642.

Journal of the American Statistical Association
|December 4, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces new statistical methods for parameter estimation in ordinary differential equation (ODE) models, addressing the inverse problem using a pseudo-least squares approach. The methods are validated through simulations and an HIV dynamics study.

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Last Updated: Jun 18, 2026

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

Area of Science:

  • Mathematical modeling
  • Statistical inference
  • Biomedical sciences

Background:

  • Differential equation (DE) models are crucial in science and engineering.
  • The forward problem (simulation) is well-studied, but the inverse problem (parameter estimation) requires advanced statistical methods.
  • Existing least squares approaches for parameter estimation in DE models have limitations.

Purpose of the Study:

  • To propose novel parameter estimation methods for ordinary differential equation (ODE) models.
  • To address the inverse problem within a measurement error regression framework.
  • To establish asymptotic properties of the proposed estimators.

Main Methods:

  • Local smoothing approach
  • Pseudo-least squares (PsLS) principle
  • Comparison with the SIMEX method
  • Finite sample performance evaluation via simulation studies

Main Results:

  • Asymptotic properties of the PsLS estimator are established.
  • The PsLS method demonstrates effectiveness in parameter estimation for ODE models.
  • Simulation studies validate the performance of the proposed methods.

Conclusions:

  • The proposed PsLS method offers a robust statistical approach for parameter estimation in ODE models.
  • The methods are applicable to real-world problems, such as HIV dynamic studies.
  • This work advances the statistical treatment of inverse problems in differential equation modeling.