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

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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.

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Acknowledgements

Wu was supported by Ministry of Science and Technology of Taiwan under grants (MOST 111-2118-M-259 -002). The work of Lim was supported by National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (NRF-2019R1A2C1002213 and 2020R1A4A1018207). The work of Yoon and Choi was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government (MSIT) (Nos. RS-2023-00221762 and 2021R1A2B5B01002620).

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Philip Guthrie Hoffman Hall 3551 Cullen Blvd, Houston, TX, 77204-3008, USA

    Hojun You

  2. The School of Mechanical Engineering, Yonsei University, 50 Yonsei Ro, Seodaemun Gu, Seoul, 03722, South Korea

    Kyubaek Yoon & Jongeun Choi

  3. Department of Applied Mathematics, National Dong Hwa University, No. 1, Section 2, Daxue Rd, Shoufeng, Hualien County, 974, Taiwan

    Wei-Ying Wu

  4. Department of Statistics, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul, 08826, South Korea

    Chae Young Lim

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  1. Hojun You
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  2. Kyubaek Yoon
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  4. Jongeun Choi
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  5. Chae Young Lim
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Correspondence to Wei-Ying Wu.

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You, H., Yoon, K., Wu, WY. et al. Regularized nonlinear regression with dependent errors and its application to a biomechanical model. Ann Inst Stat Math 76, 481–510 (2024). https://doi.org/10.1007/s10463-023-00895-1

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  • DOI: https://doi.org/10.1007/s10463-023-00895-1

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