Linear Allocation Rules under Uncertainty

Abstract

Linear models have been widely used in economic and other decision-making situations due to their simplicity and perhaps flexibility. For statistical estimation problems linearity has other advantages. In practical applications to real world data, linear models have to face two basic constraints. One is that the decision variables and sometimes the state variables have to be constrained in the sense of inequalities and hence the characterization of decision regions is very important. The second concerns the generating mechanisms of the linear model, e.g. it may be generated by a quadratic objective function as in the linear decision rule (LDR) approach [4], or in the team decision approach with a quadratic pay-off function [6, 10]; it may also be generated by the expected utility function as in stochastic linear programming [12, 18].