The decision in a data‐driven decision‐making problem is generally a high‐dimensional function of data. When can the decision be reduced to a single‐dimensional function of a statistic? This study addresses this question based on the operational statistics literature. The study introduces the notion of sufficient operational statistics and derives the factorization theorem for identifying such statistics. Further, the study proposes a solution procedure based on the statistics and derives the finite‐sample performance bound of the proposed solution.
BanG.‐Y.RudinC. (2019). The big data newsvendor: Practical insights from machine learning. Operations Research, 67(1), 90–108.
2.
ChuL. Y.ShanthikumarJ. G.ShenZ.‐J. M. (2008). Solving operational statistics via a Bayesian analysis. Operations Research Letters, 36(1), 110–116.
3.
CobbC. W.DouglasP. H. (1928). A theory of production. American Economic Review, 18(1), 139–165.
4.
JiaJ.KatokE. (2021). How do sellers set auction reserve prices based on data? (Working Paper).
5.
KrishnaV. (2010). Auction theory (2nd ed.). Academic Press.
6.
LeviR.RoundyR. O.ShmoysD. B. (2007). Provably near‐optimal sampling‐based policies for stochastic inventory control models. Mathematics of Operations Research, 32(4), 821–839.
7.
LimA. E. B.ShanthikumarJ. G.ShenZ.‐J. M. (2006). Model uncertainty, robust optimization, and learning. Tutorials in Operations Research: Models, Methods, and Applications for Innovative Decision Making, 66–94. https://doi.org/10.1287/educ.1063.0021
8.
LiyanageL. H.ShanthikumarJ. G. (2005). A practical inventory control policy using operational statistics. Operations Research Letters, 33(4), 341–348.
9.
LuM.ShanthikumarJ. G.ShenZ.‐J. M. (2015). Technical note—operational statistics: Properties and the risk‐averse case. Naval Research Logistics, 62(3), 206–214.
10.
RamamurthyV.ShanthikumarJ. G.ShenZ.‐J. M. (2012). Inventory policy with parametric demand: Operational statistics, linear correction, and regression. Production and Operations Management, 21(2), 291–308.
11.
SimonC. P.BlumeL. (1994). Mathematics for economists (Vol. 7). Norton.
