STA 290 Seminar: Gourab Mukherjee

STA 290 Seminar Series

Thursday, March 31st, 4:10pm, MSB 1147 (Colloquium Room)

Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)

Speaker:          Gourab Mukherjee (University of Southern California)

Title:                “Empirical Bayes Prediction for the Multivariate Newsvendor Loss Function”

Abstract:          Motivated by an application in supply chain management, we consider the multi-product newsvendor problem of finding the optimal stocking levels that minimize a weighted sum of the total inventory and lost sales costs. We focus on a setting where we have a large number of products and observe only noisy estimates of the underlying demand. We develop and use an Empirical Bayes methodology that minimizes a new, uniformly efficient asymptotic risk estimate.  In calculating the magnitude and direction of shrinkage, our proposed predictive rules incorporate the asymmetric nature of the piecewise linear newsvendor loss function and are shown to be asymptotically optimal. Using simulated data, we also study the non-asymptotic performance of our method. In our setting the demand distributions must be estimated from data involving a large number of products. In common with many other problems we find that empirical Bayes shrinkage provides better performance than simple coordinate-wise rules. However, the problem here differs in fundamental aspects from estimation or prediction under the weighted quadratic losses considered in much previous literature. This necessitates different strategies for creation of effective empirical Bayes predictors.