Monotonic Quantile Regression with Bernstein Polynomials for Stochastic Simulation

Quantile regression is an important tool to determine the quality level of service, product, and operation systems via stochastic simulation. It is frequently known that the quantiles of the output distribution are monotonic functions of certain inputs to the simulation model. Because there is typically high variability in estimation of tail quantiles, it can be valuable to incorporate this information in quantile modeling. However, the existing literature on monotone quantile regression with multiple inputs is sparse. In this article, we propose a class of monotonic regression models, which consists of functional analysis of variance (FANOVA) decomposition components modeled with Bernstein polynomial bases for estimating quantiles as a function of multiple inputs. The polynomial degrees of the bases for the model and the FANOVA components included in the model are selected by a greedy algorithm. Real examples demonstrate the advantages of incorporating the monotonicity assumption in quantile regression and the good performance of the proposed methodology for estimating quantiles. Supplementary materials for this article are available online.