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.
