Censored Demand Estimation in Retail

In this paper, the question of interest is estimating true demand of a product at a given store location and time period in the retail environment based on a single noisy and potentially censored observation. To address this question, we introduce a non-parametric framework to make inference from multiple time series. Somewhat surprisingly, we establish that the algorithm introduced for the purpose of "matrix completion" can be used to solve the relevant inference problem. Specifically, using the Universal Singular Value Thresholding (USVT) algorithm [2], we show that our estimator is consistent: the average mean squared error of the estimated average demand with respect to the true average demand goes to 0 as the number of store locations and time intervals increase to ınfty. We establish naturally appealing properties of the resulting estimator both analytically as well as through a sequence of instructive simulations. Using a real dataset in retail (Walmart), we argue for the practical relevance of our approach.