Constrained interval-valued linear regression model

In current interval-valued linear regression models, meaningless predictions may be generated because the lower bounds of the predicted intervals may be greater than their upper bounds. To avoid this problem, we propose a constrained interval-valued linear regression model based on random set theory. However, due to the introduction of constraints in this model, the expectation of the errors is no longer zero, and estimation provided by traditional least square may produce systematic bias. To address this issue, we introduce a two-step procedure: in the first step, a dummy variable is defined and plugged into the regression model to ensure that the expectation of errors is zero; least square estimation is then used in the second step. To show the validity of proposed method, experiments on simulated and real data are presented.

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