The choice of an estimation method has received considerable attention in the Operations Research literature. In this paper we depart from the standard use of linex and double-linex loss functions which are widely used in parameter estimation and forecasting problems and we propose a non-standard use for them. Specifically, we propose to use the corresponding linex and double-linex error densities as models for the errors of a regression problem when more emphasis should be placed on over-estimation or under-estimation of errors. The new techniques are applied to synthetic as well real data concerning the role of management in production as well as to an application of forecasting volatility in intradaily data.