Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have unspecified nonlinear effects. Significantly advancing from the existing literature, we consider a model with interactions between the functional and scalar covariates. To accommodate long-tailed error distributions which are not uncommon in data analysis, we adopt the quantile technique for estimation. To achieve more interpretable estimation, and to accommodate many practical settings, we assume that the functional covariate effects are locally sparse (that is, there exist subregions on which the effects are exactly zero), which naturally leads to a variable/model selection problem. We propose respecting the "main effect, interaction" hierarchy, which postulates that if a subregion has a nonzero effect in an interaction term, then its effect has to be nonzero in the corresponding main functional effect. For estimation, identification of local sparsity, and respect of the hierarchy, we propose a penalization approach. An effective computational algorithm is developed, and the consistency properties are rigorously established under mild regularity conditions. Simulation shows the practical effectiveness of the proposed approach. The analysis of the Tecator data further demonstrates its practical applicability. Overall, this study can deliver a novel and practically useful model and a statistically and numerically satisfactory estimation approach.
Convolution-smoothing based locally sparse estimation for functional quantile regression
Xi’an Jiaotong University（西安交通大学）；College of Physicians and Surgeons, Columbia University（哥伦比亚大学医学研究生学院）；Shanghai University of Finance and Economics（上海财经大学）；Simon Fraser University（西蒙菲莎大学）
A comparison of some conformal quantile regression methods
我们比较了最近提出的两种方法，它们结合了共形推理和分位数回归的思想，以在样本交换下产生局部自适应和边缘有效的预测区间（Romano等人，2019; Kivaranovic等人，2019年）。首先，我们证明了这两种方法是渐近有效的大样本下，在一些额外的假设。然后，我们比较他们的经验模拟和真实数据。我们的研究结果表明，Romano et al.（2019）中的方法通常在有限样本中产生更紧密的预测区间。最后，我们讨论了如何通过固定用于训练和一致化的观测的相对比例来调整这些过程。
Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networks
School of Mathematics, University of Edinburgh（爱丁堡大学数学学院）；Statistics Program, Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学计算机、电气与数学科学与工程（CEMSE）分部统计项目）
Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to first steps. We show that orthogonal moment functions can be constructed by adding to identifying moments the nonparametric influence function for the effect of the first step on identifying moments. Orthogonal moments reduce model selection and regularization bias, as is very important in many applications, especially for machine learning first steps. We gi…
