论文标题
功能性马蹄滑平滑以进行功能趋势估计
Functional Horseshoe Smoothing for Functional Trend Estimation
论文作者
论文摘要
由于仪器和计算机的发展，功能观察结果越来越流行。但是，对于一系列功能数据（例如功能时间序列），灵活估计具有有效不确定性定量的潜在趋势的有效方法仍然很少。在这项工作中，我们通过在功能变量差异的一般顺序引入收缩，开发了一种局部自适应平滑方法，称为功能马蹄平滑。这使我们能够通过充分利用收缩能力来捕捉突然的变化，并通过贝叶斯推论评估不确定性。完全贝叶斯框架允许通过后验预测损失选择基本函数的数量。我们提供了支持收缩能力的模型的理论特性。同样，通过利用功能数据的性质，该方法能够处理异质观察的数据而无需扩大数据。仿真研究和实际数据分析表明，所提出的方法具有理想的特性。
Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of functional data (e.g. functional time series) are still scarce. In this work, we develop a locally adaptive smoothing method, called functional horseshoe smoothing, by introducing a shrinkage prior to the general order of differences of functional variables. This allows us to capture abrupt changes by making the most of the shrinkage capability and also to assess uncertainty by Bayesian inference. The fully Bayesian framework allows the selection of the number of basis functions via the posterior predictive loss. We provide theoretical properties of the model, which support the shrinkage ability. Also, by taking advantage of the nature of functional data, this method is able to handle heterogeneously observed data without data augmentation. Simulation studies and real data analysis demonstrate that the proposed method has desirable properties.
