Error Propagation in Asymptotic Analysis of the Data-Driven (s, S) Inventory Policy
研究了数据驱动(s,S)库存策略中因误差传播导致的统计性质变化，提出了多样本U过程的渐近表示，用于推导参数影响函数和联合渐近正态性，并给出了样本量确定和区间估计等应用。
Estimating Optimal Inventory Policies: Moving Beyond SAA and Empirical Process Theory In “Error Propagation in Asymptotic Analysis of the Data-Driven (s,S) Inventory Policy,” Zhang, Ye, and Haskell dive into the class multiperiod stochastic inventory control in a data-driven setting. They investigate the statistical properties of the data-driven $(s, S)$-policy obtained by recursively computing the empirical cost-to-go functions. In this setting, the empirical cost-to-go functions for the estimated parameters are not i.i.d. sums because of the error propagation. They establish a novel asymptotic representation for multi-sample $U$-processes in terms of i.i.d. sums. This representation enables them to apply empirical process theory to derive the influence functions of the estimated parameters and to establish joint asymptotic normality. Based on these results, they also propose an entirely data-driven estimator of the optimal expected cost and derive its asymptotic distribution. They demonstrate some useful applications of their asymptotic results, including sample size determination and interval estimation.