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LINEAR REGRESSION OF interval-valued data BASED ON COMPLETE INFORMATION IN HYPERCUBES

Journal of Systems Science and Systems Engineering 2012年第4期21卷 422-442页

作者： Huiwen WANG Rong GUAN Junjie WU Beijing Key Laboratory of Emergency Support Simulation Technologies for City Operations School of Economics and ManagementBeihang University

Recent years have witnessed an increasing interest in interval-valued data analysis. As one of the core topics, linear regression attracts particular attention. It attempts to model the relationship between one or more explanatory variables and a response variable by fitting a linear equation to the interval-valued observations. Despite of the well-known methods such as CM, CRM and CCRM proposed in the literature, further study is still needed to build a regression model that can capture the complete information in interval-valued observations. To this end, in this paper, we propose the novel Complete Information Method （CIM） for linear regression modeling. By dividing hypercubes into informative grid data, CIM defines the inner product of interval-valued variables, and transforms the regression modeling into the computation of some inner products. Experiments on both the synthetic and real-world data sets demonstrate the merits of CIM in modeling interval-valued data, and avoiding the mathematical incoherence introduced by CM and CRM.

关键词： interval-valued data linear regression complete information method (CIM) hypercubes

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A Constrained interval-valued Linear Regression Model:A New Heteroscedasticity Estimation Method

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Journal of Systems Science & Complexity 2020年第6期33卷 2048-2066页

作者： ZHONG Yu ZHANG Zhongzhan LI Shoumei Beijing University of Technology College of Applied SciencesBeijing 100020China

Linear regression models for interval-valued data have been widely *** literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,and fit two separate real-valued or two dimension linear regression *** paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix,based on a generalized linear model for interval-valued data.A three step estimation method is *** conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.

关键词： Conditional maximum likelihood estimation interval-valued data order constraint truncated normal distribution weighted least squares estimation

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