Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional data, we propose a set of conformal predictors that produce finite-sample either valid or exact multivariate simultaneous prediction bands under the mild assumption of exchangeable regression pairs. The fact that the prediction bands can be built around any regression estimator and that can be easily found in closed form yields a very widely usable method, which is fairly straightforward to implement. In addition, we first introduce and then describe a specific conformal predictor that guarantees an asymptotic result in terms of efficiency and inducing prediction bands able to modulate their width based on the local behavior and magnitude of the functional data. The method is investigated and analyzed through a simulation study and a real-world application in the field of urban mobility.
Neural Optimal Transport Meets Multivariate Conformal Prediction
Department of ML, MBZUAI（机器学习系，MBZUAI）；MBZUAI, UAE（MBZUAI，阿联酋）；CMAP, École polytechnique（CMAP，巴黎高等理工学院）；Ecole Polytechnique, Palaiseau, France（巴黎高等理工学院，Palaiseau，法国）
Minimum Volume Optimal Transport for Multivariate Conformal Prediction
School of Statistics and Data Science, Nankai University（南开大学统计与数据科学学院）；School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；School of Management, Fudan University（复旦大学管理学院）
A Formal Graphical Inference Framework for Combining Effect Size with Statistical Significance: Application to Multivariate and Functional Linear Models
Faculty of Agriculture and Technology, University of South Bohemia（南波希米亚大学农业与技术学院）；Natural Resources Institute Finland (Luke)（芬兰自然资源研究所（Luke））；University of Helsinki（赫尔辛基大学）
Global Depths for Irregularly Observed Multivariate Functional Data
Two frameworks for multivariate functional depth based on multivariate depths are introduced in this paper. The first framework is multivariate functional integrated depth, and the second framework involves multivariate functional extremal depth, which is an extension of the extremal depth for univariate functional data. In each framework, global and local multivariate functional depths are proposed. The properties of population multivariate functional depths and consistency of finite sample depths to their population versions are established. In addition, finite sample depths under irregularl…
Graphical Principal Component Analysis of Multivariate Functional Time Series
School of Mathematics, Sun Yat-sen University（中山大学数学学院）；Center for Applied Statistics and School of Statistics, Renmin University of China（中国人民大学统计学院，应用统计中心）
Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data
Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya（马来亚大学理学院数学科学研究所）；Universiti Malaya Centre for Data Analytics, Universiti Malaya（马来亚大学数据分析中心）；Center of Research for Statistical Modelling and Methodology, Faculty of Science, Universiti Malaya（马来亚大学理学院统计建模与方法研究中心）；Institut de Mathématiques de Bordeaux, UMR 5251, CNRS, Université de Bordeaux, Bordeaux INP（波尔多大学波尔多数学研究所）；Mathematics, Division of Science, New York University Abu Dhabi（纽约大学阿布扎比分校理学院数学系）；CNRS, UMR 8524–Laboratoire Paul Painlevé, Inria-Datavers, Université de Lille（里尔大学保罗·潘勒瓦数学研究中心）；Independent Researcher（独立研究者）
A General Framework for Multivariate Functional Principal Component Analysis of Amplitude and Phase Variation
函数数据通常包含幅度和相位变化。在许多数据情况下，相位变化被视为滋扰效应，并在预处理过程中被删除，尽管它可能包含有价值的信息。本文主要研究幅度和相位变化的联合主成分分析。由于翘曲函数空间具有复杂的几何结构，分析的一个关键要素是将翘曲函数转换为$L^2(\mathcal{T})$。我们提出了不同的转换方法，并展示了它们如何适合一般的转换类。这使我们能够比较它们的优势和局限性。在PCA的背景下，我们的研究结果提供了参数，有利于集中的对数比变换。我们进一步将Hadjipantelis et al.（2015）和Lee and Jung（2017）的现有方法嵌入到多变量函数PCA的框架中，其中我们研究了基于适当度量的估计器的特性。该方法是通过应用地震说明。
Sparse Functional Boxplots for Multivariate Curves
This paper introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate functional data. The sparse functional boxplot, based on the functional boxplot, displays sparseness proportions within the 50\% central region. The intensity sparse functional boxplot indicates the relative intensity of fitted sparse point patterns in the central region. The two-stage functional boxplot, which derives from the functional boxplot to detect outl…
