Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods to analyze interval-valued data results in loss of information, and thus, several interval-valued data models have been proposed to gather reliable information from such data types. On the other hand, recent technological developments have led to high dimensional and complex data in many application areas, which may not be analyzed by traditional techniques. Functional data analysis is one of the most commonly used techniques to analyze such complex datasets. While the functional extensions of much traditional statistical techniques are available, the functional form of the interval-valued data has not been studied well. This paper introduces the functional forms of some well-known regression models that take interval-valued data. The proposed methods are based on the function-on-function regression model, where both the response and predictor/s are functional. Through several Monte Carlo simulations and empirical data analysis, the finite sample performance of the proposed methods is evaluated and compared with the state-of-the-art.
Covariance Matrix Estimation for High-Dimensional Interval-Valued Data with Positive Definiteness
Peking University（北京大学）；Beihang University（北京航空航天大学）；Renmin University of China（中国人民大学）；Southern University of Science and Technology（南方科技大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；University of Science and Technology of China（中国科学技术大学）；PKU-Wuhan Institute for Artificial Intelligence（北京大学武汉人工智能研究院）；Xiangjiang Laboratory（湘江实验室）；Guanghua School of Management, Peking University（北京大学光华管理学院）
Projection-Based Outlier Detection in Interval-Valued Functional Data
School of Economics and Management, Beihang University（北京航空航天大学经济管理学院）；Key Laboratory of Complex System Analysis, Management and Decision (Beihang University)（复杂系统分析与决策重点实验室（北京航空航天大学））；Advanced Institute of Information Technology, Peking University（北京大学前沿交叉学科研究院信息科技前沿中心）；Wangxuan Institute of Computer Technology, Peking University（北京大学王选计算机研究所）
Estimating Precision Matrices for High-Dimensional Interval-Valued Data
School of Economics and Management, Beihang University（北京航空航天大学经济管理学院）；Key Laboratory of Complex System Analysis, Management and Decision (Beihang University)（复杂系统分析与决策重点实验室（北京航空航天大学））；Advanced Institute of Information Technology, Peking University（北京大学信息科学技术学院前沿交叉研究院）；Wangxuan Institute of Computer Technology, Peking University（北京大学王选计算机研究所）
Minimum Covariance Determinant Estimator and Outlier Detection for Interval-valued Data
Instituto Superior Técnico, Universidade de Lisboa（里斯本理工大学）；Faculdade de Economia e Gestão, Universidade do Porto（波尔图大学经济管理学院）；LIAAD-INESC TEC（INESC TEC LIAAD实验室）
