结果依赖缺失下稀疏采样Gauss-Markov过程的推断
Inference for sparsely sampled Gauss-Markov processes under outcome-dependent dropout
AI总结：
针对结果依赖缺失下的稀疏采样Gauss-Markov过程，提出基于似然的估计框架，避免偏差并达到极小极大最优速率，应用于肿瘤生长数据。
AI中文摘要：
我们考虑由线性随机微分方程（SDE）建模的潜在Gauss-Markov过程生成的稀疏观测函数型数据。受肿瘤生长数据应用的启发，我们允许结果依赖的缺失机制，即一旦最近一次观测超过预设阈值，采样即终止。此类观测方案在纵向研究中自然出现，并违反了部分观测函数型数据分析中通常假设的完全随机缺失这一基本假设。我们开发了一个基于似然的估计框架，与现有的基于矩的方法相比，该框架避免了由结果依赖缺失引起的偏差。我们建立了所提出估计量的收敛速率，并证明它们在达到对数因子意义下是极小极大最优的，且在SDE的随机初始条件下，扩散系数的收敛速率快于漂移系数。对肿瘤生长数据的应用进一步展示了全概率函数型数据模型在二阶推断之外任务中的优势，包括预测带、首达时间和肿瘤年龄估计。
英文摘要：
We consider sparsely observed functional data generated by a latent Gauss-Markov process modeled through a linear stochastic differential equation (SDE). Motivated by an application to tumor growth data, we allow for outcome-dependent dropout, where sampling terminates once the most recent observation exceeds a prescribed threshold. Such observation schemes arise naturally in longitudinal studies and violate the fundamental missing completely at random assumption commonly imposed in the analysis of partially observed functional data. We develop a likelihood-based estimation framework that, in contrast to existing moment-based methods, avoids the bias induced by outcome-dependent dropout. We establish convergence rates for the proposed estimators and show that they are mini-max optimal up to logarithmic factors, with the diffusion coefficient admitting a faster rate than the drift coefficients under a random initial condition for the SDE. An application to tumor growth data further demonstrates the advantages of a fully probabilistic functional data model for tasks beyond second-order inference, including prediction bands, first-passage times, and tumor-age estimation.
