Joint Estimation of the Arrival Rate and Customer Taste Coefficients From Censored Transactional Data
研究从删失交易数据中联合估计顾客到达率和嵌套Logit模型参数，提出一种序列极小化最大化算法，在合成和真实数据上优于基准方法。
This work aims to jointly estimate the arrival rate of customers to a market and the nested logit model that forecasts hierarchical customer choices from an assortment of products. The estimation is based on censored transactional data, where lost sales are not recorded. The goal is to determine the arrival rate, customer taste coefficients, and nest dissimilarity parameters that maximize the likelihood of the observed data. The problem is formulated as a maximum likelihood estimation model that addresses two prevailing challenges in the existing literature: Estimating demand from data with unobservable lost sales and capturing customer taste heterogeneity arising from hierarchical choices . However, the model is intractable to solve or analyze due to the nonconcavity of the likelihood function in both taste coefficients and dissimilarity parameters. We characterize conditions under which the model parameters are identifiable. Our results reveal that the parameter identification is influenced by the diversity of products and nests . We also develop a sequential minorization-maximization algorithm to solve the problem, by which the problem boils down to solving a series of convex optimization models with simple structures. Then, we show the convergence of the algorithm by leveraging the structural properties of these models. We evaluate the performance of the algorithm by comparing it with widely used benchmarks, using both synthetic and real data. Our findings show that the algorithm consistently outperforms the benchmarks in maximizing in-sample likelihood and ranks among the top two in out-of-sample prediction accuracy. Moreover, our algorithm is particularly effective in estimating nested logit models with low dissimilarity parameters, yielding higher profitability compared to the benchmarks.