Empirical dynamics for longitudinal data
纵向数据的经验动态建模AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要明确研究多个个体或实验单位的稀疏纵向重复测量，与面板数据的观测结构直接相关。
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关注这篇论文的作者
纵向数据的经验动态建模
- 研究问题
- 对于稀疏且含噪声的个体纵向观测，如何从数据获得时变系数的一阶随机微分方程，并描述轨迹偏离确定性近似的程度？
- 方法与思路
- 作者非参数估计动态方程的组成，将过程导数分解为时变线性方程解释的部分与正交漂移部分，并估计轨迹及漂移方差。
- 材料陈述的贡献
- 摘要称改进扰动分析得到特征函数导数估计的更好渐近速率，并建立时变系数与漂移组成的一致性，以在线拍卖数据示例说明。
- 阅读关注点
- 核对平滑轨迹、稀疏观测和噪声条件，辨明动态分解的统计解释，并检查导数估计、漂移方差及收敛速率的具体要求。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；观测设计和正则条件未说明，经验动态分解不能直接解释为因果机制或结构性拍卖模型。
原文摘要
We demonstrate that the processes underlying on-line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time-varying coefficients and a smooth drift process. This equation may be empirically obtained from longitudinal observations for a sample of subjects and does not presuppose specific knowledge of the underlying processes. For the nonparametric estimation of the components of the differential equation, it suffices to have available sparsely observed longitudinal measurements which may be noisy and are generated by underlying smooth random trajectories for each subject or experimental unit in the sample. The drift process that drives the equation determines how closely individual process trajectories follow a deterministic approximation of the differential equation. We provide estimates for trajectories and especially the variance function of the drift process. At each fixed time point, the proposed empirical dynamic model implies a decomposition of the derivative of the process underlying the longitudinal data into a component explained by a linear component determined by a varying coefficient function dynamic equation and an orthogonal complement that corresponds to the drift process. An enhanced perturbation result enables us to obtain improved asymptotic convergence rates for eigenfunction derivative estimation and consistency for the varying coefficient function and the components of the drift process. We illustrate the differential equation with an application to the dynamics of on-line auction data.