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Abstract:
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We study the traditional newsvendor problem in the modern big data regime. The objective is to develop a data-driven policy that minimizes a weighted sum of the total inventory and lost sales costs. We develop and use an Empirical Bayes methodology that minimizes a new, uniformly efficient asymptotic risk estimate. Using simulated data, we also study the non-asymptotic performance of our method. The methods developed here can also be used to get optimal empirical Bayes predictive strategies for general piecewise linear and related asymmetric loss. 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 respects 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. The hyper-parameter estimator we develop involves an appropriate use of Hermite polynomial expansions for the relevant stochastic functions.
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