An adaptive estimator is proposed to optimally estimate unknown truncation points of the error support space for the general linear model. The adaptive estimator is specified analytically to minimize a risk function based on the squared error loss measure. It is then empirically applied to a generalized maximum entropy estimator of the linear model using bootstrapping, allowing the information set of the model itself to determine the truncation points. Monte Carlo simulations are used to demonstrate performance of the adaptive entropy estimator relative to maximum entropy estimation coupled with alternative truncation rules and to ordinary least squares estimation. A food demand application is included to demonstrate practical implementation of the adaptive estimator.