Measuring the Goodness of Orthogonal Array Discretizations for High-Dimensional Continuous-State Stochastic Dynamic Programs

This paper describes a state space discretization scheme based on statistical experimental designs generated from orthogonal arrays of strength three with index unity. Chen et al. (1999) employed this eecient discretization scheme in a numerical solution method for high-dimensional continuous-state stochastic dynamic programming (SDP). These OAs are instrumental in reducing the dimensionality of continuous-state SDP. In particular, computationally eecient space-lling measures for these OAs are derived for evaluating how well a speciic OA discretization lls the state space. Comparisons were made with two types of common measures: ones which maximize the average (or minimum) distance between discretization points within the OA and ones which minimize the average (or maximum) distance between discretization points and nondiscretization points lying on a full grid (i.e., points lying on the full grid that are not contained in the OA discretization). OAs of strength three were tested by tting multivariate adaptive regression splines to data from an inventory forecasting continuous-state stochastic dynamic program.