Model Mis-Specification in Newsvendor Decisions: A Comparison of Frequentist Parametric, Bayesian Parametric and Nonparametric Approaches
Model Mis-Specification in Newsvendor Decisions: A Comparison of Frequentist Parametric, Bayesian Parametric and Nonparametric Approaches
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报童决策中的模型错误指定：频率派参数、贝叶斯参数和非参数方法的比较
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发表时间：
2020
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通讯作者：
Fabian Taigel
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作者：
Gah;Zhenyu Gao;Fabian Taigel
我们比较了过去文献中研究的三种不同的数据驱动的库存优化方法-频率参数（FP），贝叶斯参数（BP）和非参数-报童问题。对于参数方法，我们允许需求模型的错误指定。我们证明了，在温和的正则性条件下，（i）FP和BP的渐近偏差和方差公式是等价的，（ii）错误指定的参数方法产生渐近有偏的决定，不同于正确指定的参数方法和非参数方法，和（iii）错误指定的参数方法的渐近方差收敛到零的速率$1/n$，与正确指定的参数方法和非参数方法的1/n^2$比率相反，其中$n$是需求样本的数量。然后，我们表明，对于九对假设与真实的需求分布对，（iv）渐近偏差和方差公式近似有限样本对应物非常好，（v）正确指定的参数方法在决策和成本的渐近均方误差（AMSE）中占主导地位，以及（vi）令人惊讶的是，在决策和成本的AMSE中，错误指定的参数方法有可能主导非参数方法。我们比较的方法从一个大型的新鲜食品链的数据集，并讨论了选择“最佳”的方法的细微差别。
We compare three different approaches studied by past literature on data-driven inventory optimization--- Frequentist Parametric (FP), Bayesian Parametric (BP) and Nonparametric--- for the newsvendor problem. For the Parametric approaches, we allow for mis-specification of the demand model. We prove, under mild regularity conditions, (i) asymptotic bias and variance formulas of FP and BP are equivalent, (ii) 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 $1/n$, in contrast to the $1/n^2$ rate for the correctly-specified Parametric approaches and the Nonparametric approach, where $n$ is the number of demand samples. We then show, for nine pairs of assumed versus true demand distribution pairs, (iv) asymptotic bias and variance formulas approximate finite-sample counterparts very well, (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 compare the approaches on a dataset from a large fresh food chain, and discuss the nuances of choosing the ``best' approach.