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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hojun You & Kyubaek Yoon & Wei-Ying Wu & Jongeun Choi & Chae Young Lim, 2024. "Regularized nonlinear regression with dependent errors and its application to a biomechanical model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(3), pages 481-510, June.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:3:d:10.1007_s10463-023-00895-1
    DOI: 10.1007/s10463-023-00895-1
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