摘要翻译：
多项式Logit模型及其所满足的公理无关方案的独立性(IIA)是离散选择中应用最广泛的工具。MNL模型作为各种领域的主要模型，但也受到广泛批评，大量实验文献声称记录了IIA不成立的现实世界环境。在过去的几十年里，作为模型假设的国际投资协定的统计检验一直是许多实际检验的主题，重点是对国际投资协定的具体偏差，但对国际投资协定假设检验的形式大小性质仍然不太了解。在这项工作中，我们用严格的悲观主义取代了文献中的一些模糊性，证明了任何具有低最坏情况误差的IIA的一般检验都需要数量与选择问题的备选方案数量成指数关系的样本。与以前的工作相比，我们的分析的一个主要好处是它完全位于有限样本域，这是理解离散选择的常见数据贫乏设置中测试行为的一个关键特征。我们的下限是与结构相关的，作为乐观的潜在原因，我们发现，如果一个人将IIA的检验限制在可能发生在一个特定的选择集合（例如，对）中的违规行为，我们就会得到与结构相关的下限，这些下限的悲观程度要低得多。我们对这个测试问题的分析是非传统的，因为它是高度组合的，计算了从选择的数据集构造的特定二分图的循环分解的欧拉方向。通过确定给定测试问题的比较结构与其样本效率之间的基本关系，我们希望这些关系将有助于为严格地重新思考IIA测试问题以及离散选择中的其他测试问题奠定基础。
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英文标题：
《Fundamental Limits of Testing the Independence of Irrelevant
  Alternatives in Discrete Choice》
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作者：
Arjun Seshadri, Johan Ugander
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最新提交年份：
2020
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  The Multinomial Logit (MNL) model and the axiom it satisfies, the Independence of Irrelevant Alternatives (IIA), are together the most widely used tools of discrete choice. The MNL model serves as the workhorse model for a variety of fields, but is also widely criticized, with a large body of experimental literature claiming to document real-world settings where IIA fails to hold. Statistical tests of IIA as a modelling assumption have been the subject of many practical tests focusing on specific deviations from IIA over the past several decades, but the formal size properties of hypothesis testing IIA are still not well understood. In this work we replace some of the ambiguity in this literature with rigorous pessimism, demonstrating that any general test for IIA with low worst-case error would require a number of samples exponential in the number of alternatives of the choice problem. A major benefit of our analysis over previous work is that it lies entirely in the finite-sample domain, a feature crucial to understanding the behavior of tests in the common data-poor settings of discrete choice. Our lower bounds are structure-dependent, and as a potential cause for optimism, we find that if one restricts the test of IIA to violations that can occur in a specific collection of choice sets (e.g., pairs), one obtains structure-dependent lower bounds that are much less pessimistic. Our analysis of this testing problem is unorthodox in being highly combinatorial, counting Eulerian orientations of cycle decompositions of a particular bipartite graph constructed from a data set of choices. By identifying fundamental relationships between the comparison structure of a given testing problem and its sample efficiency, we hope these relationships will help lay the groundwork for a rigorous rethinking of the IIA testing problem as well as other testing problems in discrete choice.
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PDF链接：
https://arxiv.org/pdf/2001.07042