论文标题
新型非线性动态功能/纵向数据模型的统一统计推断
Unified statistical inference for a novel nonlinear dynamic functional/longitudinal data model
论文作者
论文摘要
鉴于最近研究大量功能/纵向数据的工作，例如来自COVID-19大流行的最终数据，我们提出了一种新型的功能/纵向数据模型，该模型是流行的变化系数（VC）模型和加性模型的组合。我们称其为半VCAM，其中响应可能是功能/纵向变量，解释性变量可能是功能/纵向和标量变量的混合物。值得注意的是，某些标量变量也可能是分类变量。半VCAM同时允许具有实质性的灵活性和维持一维收敛速率。开发了借助初始B条线系列近似的局部线性平滑，以估计模型中未知的功能效应。为了避免数据的稀疏和密集情况之间的主观选择，我们在稀疏，密集和超密集的数据案例的统一框架上建立了基于飞行员估计的局部线性估计器（PEBLLE）的渐近理论。此外，我们构建了统一的一致测试，以证明简短的子模型是否足够。这些测试方法还避免了数据的稀疏，致密和超密集情况之间的主观选择。广泛的蒙特卡洛模拟研究研究了所提出方法的有限样本性能证实了我们的渐近结果。我们通过分析中国的COVID-19数据和CD4数据进一步说明了我们的方法论。
In light of recent work studying massive functional/longitudinal data, such as the resulting data from the COVID-19 pandemic, we propose a novel functional/longitudinal data model which is a combination of the popular varying coefficient (VC) model and additive model. We call it Semi-VCAM in which the response could be a functional/longitudinal variable, and the explanatory variables could be a mixture of functional/longitudinal and scalar variables. Notably some of the scalar variables could be categorical variables as well. The Semi-VCAM simultaneously allows for both substantial flexibility and the maintaining of one-dimensional rates of convergence. A local linear smoothing with the aid of an initial B spline series approximation is developed to estimate the unknown functional effects in the model. To avoid the subjective choice between the sparse and dense cases of the data, we establish the asymptotic theories of the resultant Pilot Estimation Based Local Linear Estimators (PEBLLE) on a unified framework of sparse, dense and ultra-dense cases of the data. Moreover, we construct unified consistent tests to justify whether a parsimony submodel is sufficient or not. These test methods also avoid the subjective choice between the sparse, dense and ultra dense cases of the data. Extensive Monte Carlo simulation studies investigating the finite sample performance of the proposed methodologies confirm our asymptotic results. We further illustrate our methodologies via analyzing the COVID-19 data from China and the CD4 data.
