Regularized nonlinear regression with dependent errors and its application to a biomechanical model

A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that the data from a head-neck position tracking system, one of biomechanical models, show multiplicative time-dependent errors, we develop a modified penaliz...

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Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics 2024-06, Vol.76 (3), p.481-510
Main Authors: You, Hojun, Yoon, Kyubaek, Wu, Wei-Ying, Choi, Jongeun, Lim, Chae Young
Format: Article
Language:English
Subjects:
Asymptotic properties
Biomechanics
Economics
Error analysis
Finance
Insurance
Management
Mathematical models
Mathematics and Statistics
Parameter estimation
Statistics
Statistics for Business
Time dependence
Tracking systems
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Summary:A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that the data from a head-neck position tracking system, one of biomechanical models, show multiplicative time-dependent errors, we develop a modified penalized weighted least squares estimator. The proposed method can be also applied to a model with possible non-zero mean time-dependent additive errors. Asymptotic properties of the proposed estimator are investigated under mild conditions on a weight matrix and the error process. A simulation study demonstrates that the proposed estimation works well in both parameter estimation and selection with time-dependent error. The analysis and comparison with an existing method for head-neck position tracking data show better performance of the proposed method in terms of the variance accounted for.
ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-023-00895-1