We consider modeling non-autonomous dynamical systems for a group of subjects. The proposed model involves a common baseline gradient function and a multiplicative time-dependent subject-specific effect that accounts for phase and amplitude variations in the rate of change across subjects. The baseline gradient function is represented in a spline basis and the subject-specific effect is modeled as a polynomial in time with random coefficients. We establish appropriate identifiability conditions and propose an estimator based on the hierarchical likelihood. We prove consistency and asymptotic normality of the proposed estimator under a regime of moderate-to-dense observations per subject. Simulation studies and an application to the Berkeley Growth Data demonstrate the effectiveness of the proposed methodology.

中文翻译：

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为特定主题的非自主动力学建模。

我们考虑为一组主题建模非自治动力系统。所提出的模型涉及一个共同的基线梯度函数和一个与时间相关的特定于对象的乘性效应，该效应说明了对象间变化率的相位和幅度变化。基线梯度函数以样条曲线形式表示，特定对象的效果被建模为具有随机系数的时间多项式。我们建立适当的可识别性条件，并根据分层的可能性提出一个估计量。我们证明了在每个对象的中密度观测值下，拟议估计量的一致性和渐近正态性。仿真研究和对伯克利增长数据的应用证明了所提出方法的有效性。