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Activity Number: 157
Type: Topic Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #318855
Title: Empirical Bayes Prediction Under Check Loss
Author(s): Gourab Mukherjee*
Companies: University of Southern California
Keywords: check loss ; empirical bayes ; prediction ; high-dimensional ; asymptotic optimality ; oracle inequality

We develop new Empirical Bayes methods to deal with asymmetric check losses which often arise in modern business problems. Prediction under this loss function differs in fundamental respects from estimation or prediction under the somewhat well-studied weighted-quadratic loss function. In particular, the methods developed here are directly used to provide statistical estimates of the optimal stocking quantities that modern-day retailers, who sell thousands to millions of different product types, must keep in their inventories. The challenge here is to balance the tradeoffs between stocking too much and incurring high inventory cost versus stocking too little and suffering lost sales, cumulatively over all the products which results in high-dimensionality. The check loss function arises here as prediction of future demands based on past sales data needs to be done under a piecewise linear loss that penalizes underestimation and overestimation in different ways. We develop asymptotically optimal Empirical Bayes methodologies for predicting stocking levels by linear shrinkage strategies which are constructed by minimizing uniformly efficient asymptotic risk estimates.

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