Combinatorial Inference on the Optimal Assortment in Multinomial Logit Models
Dr. Shuting Shen
Postdoctoral Associate in Decision Science
The Fuqua School of Business
Duke University
Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. This paper proposes a novel inferential framework for testing such properties. We consider the widely adopted multinomial logit (MNL) model, where we assume that each customer will purchase an item within the offered products with a probability proportional to the underlying preference score associated with the product. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. By approximating the distribution of the maximum statistic with multiplier bootstrap techniques, we propose a valid testing procedure. We also conduct numerical experiments to assess the performance of our method.
Shuting Shen is currently serving as a postdoctoral research fellow under the joint supervision of Dr. Ethan X. Fang and Dr. Alexandre Belloni at Duke University’s Department of Biostatistics & Bioinformatics and Fuqua School of Business. Her research primarily revolves around operations research, large-scale inference, and distributed computing. In 2023, Shuting earned her Ph.D. in Biostatistics from Harvard University, where she worked under the guidance of Dr. Xihong Lin and Dr. Junwei Lu. Prior to her time at Harvard, Shuting completed her B.Sc. degree in mathematics and a BA degree in English (biomedicine track) at Peking University in 2018.
