Model Mis-Specification in Newsvendor Decisions: A Comparison of Frequentist Parametric, Bayesian Parametric and Nonparametric Approaches
32 Pages Posted: 1 Jan 2020
Date Written: December 14, 2019
Past literature on data-driven inventory models have taken three distinct approaches: Frequentist Parametric (FP), Bayesian Parametric (BP) and Nonparametric. In this paper, we compare across the three approaches for the newsvendor problem. For the two Parametric approaches, we consider both correct and incorrect specifications of the true demand model. We prove, under mild regularity conditions, (i) asymptotic bias and variance formulas of FP and BP are equivalent, (ii) the mis-specified Parametric approaches yield asymptotically biased decisions, unlike the correctly-specified Parametric approaches and the Nonparametric approach, and (iii) asymptotic variance of the mis-specified Parametric approaches converges to zero at rate $1/n$, whereas the rate is $1/n^2$ for the correctly-specified Parametric approaches and the Nonparametric approach. We then show, for nine pairs of assumed versus true demand distribution pairs, (iv) asymptotic bias and variance formulas for all approaches approximate finite-sample bias and variance very well, from $n$ greater than about 50, (v) correctly-specified Parametric approaches dominate the Nonparametric approach in the asymptotic mean-squared error (AMSE) of the decision and the cost, and (vi) surprisingly, it is possible for mis-specified Parametric approaches to dominate the Nonparametric approach in the AMSE of the decision and the cost. We also compare the performance of the three approaches on empirical demand distributions obtained from a large fresh food chain, and find that all methods are viable in a stationary, "business-as-usual'' setting.
Keywords: data-driven decision-making, newsvendor, inventory, model mis-specification, asymptotic statistics
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