Assessment and modeling of Interval-Valued Variables in Generalized Linear Models

Interval-valued data are observed as ranges instead of single values and contain richer information thansingle-valued data. Meanwhile, interval-valued data are used for interval-valued characteristics. An intervalgeneralized linear model is proposed for the first time in this research. Then a suitable model is presented toestimate the parameters of the interval generalized linear model. The two models are provided on the basis ofthe interval arithmetic. The estimation procedure of the parameters of the suitable model is as the estimationprocedure of the parameters of the interval generalized linear model. The least-squares (LS) estimation of thesuitable model is developed according to a nice distance in the interval space. The LS estimation is resolvedanalytically through a constrained minimization problem. Then some desirable properties of the estimatorsare checked. Finally, both the theoretical and the empirical performance of the estimators are investigated.

Keywords:

Interval-valued data , Interval arithmetic , Interval generalized linear model , Least squares estimation