Journal of Systems Science and Complexity ( IF 2.1 ) Pub Date : 2020-08-04 , DOI: 10.1007/s11424-020-9075-2 Yu Zhong , Zhongzhan Zhang , Shoumei Li
Linear regression models for interval-valued data have been widely studied. Most 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 models. This 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 proposed. Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.
中文翻译:
约束区间值线性回归模型:一种新的异方差估计方法
区间值数据的线性回归模型已得到广泛研究。大多数文献都将一个间隔分成两个实数,即该端点的左端点和右端点或该间隔的中心和半径,并拟合两个单独的实数值或二维线性回归模型。本文基于区间值数据的广义线性模型,通过对响应区间和加权线性最小二乘法的端点施加阶跃约束(带有估计的协方差矩阵),重点研究了偏差校正和异方差调整的模型。提出了一种三步估计方法。理论结论和数值评估表明,所提出的估计器比以前的估计器具有更高的效率。