Functional Horseshoe Smoothing for Functional Trend Estimation
Functional Horseshoe Smoothing for Functional Trend Estimation
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DOI：
10.5705/ss.202022.0297
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发表时间：
2022-04
影响因子：
1.4
通讯作者：
Tomoya Wakayama;S. Sugasawa
中科院分区：
文献类型：
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作者：
Tomoya Wakayama;S. Sugasawa
由于仪器和计算机的发展，功能观察越来越流行。然而，通过对一系列功能数据（例如功能时间序列）进行有效的不确定性量化来灵活估计潜在趋势的有效方法仍然很少。在这项工作中，我们通过在函数变量差异的一般顺序之前引入收缩，开发了一种局部自适应平滑方法，称为函数马蹄平滑。这使我们能够通过充分利用收缩能力来捕获突变，并通过贝叶斯推理来评估不确定性。完全贝叶斯框架允许通过后验预测损失选择基函数的数量。我们提供了模型的理论属性，支持收缩能力。此外，通过利用函数数据的性质，该方法能够处理异构观察数据而无需数据增强。仿真研究和真实数据分析表明所提出的方法具有理想的性能。
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.