Efficient stratified sampling implementations in multiresponse simulation

Often the accurate estimation of multiple values from a single simulation is of practical importance. Among the many variance reduction methods known in the literature, stratified sampling is especially useful for such a task as the allocation fractions can be used as decision variables to minimize the overall error of all estimates. Two different classes of overall error functions are proposed. The first, including the mean squared absolute and the mean squared relative error, allows for a simple closed-form solution. For the second class of error functions, including the maximal absolute and the maximal relative error, a simple and fast heuristic is proposed. The application of the new method, called “multiresponse stratified sampling”, and its performance are demonstrated with numerical examples.