A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that 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 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 (VAF).

翻译：生物力学模型通常需要在已知但复杂的非线性函数中进行参数估计与选择。受头颈位置追踪系统（一种生物力学模型）数据呈现乘性时间相关误差的启发，我们开发了一种修正的惩罚加权最小二乘估计方法。该方法也可应用于具有非零均值时间相关加性误差的模型。在权重矩阵和误差过程的温和条件下，我们研究了所提估计量的渐近性质。模拟研究表明，该估计方法在处理时间相关误差时的参数估计与选择方面表现良好。针对头颈位置追踪数据的分析及与现有方法的比较表明，所提方法在方差解释率（VAF）指标上具有更优性能。