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

Hojun You, Kyubaek Yoon, Wei-Ying Wu (), Jongeun Choi and Chae Young Lim
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Hojun You: University of Houston
Kyubaek Yoon: Yonsei University
Wei-Ying Wu: National Dong Hwa University
Jongeun Choi: Yonsei University
Chae Young Lim: Seoul National University

Annals of the Institute of Statistical Mathematics, 2024, vol. 76, issue 3, No 5, 510 pages

Abstract: Abstract 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.

Keywords: Nonlinear regression; Temporal dependence; Multiplicative error; Local consistency and oracle property (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10463-023-00895-1

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