基于最优传输的形状约束密度估计

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摘要翻译：
约束最大似然密度估计器以满足足够强的约束，$\log-$convity是一个常见的例子，具有恢复一致性的效果，而不需要额外的参数。由于经济学中的许多结果要求密度满足正则性条件，这些估计量对于经济模型的结构估计也很有吸引力。在Bagnoli和Bergstrom(2005)和Ewerhart(2013)提供的所有正则性条件的例子中，$\log-$convity足以确保密度满足要求的条件。然而，在许多情况下，$\log-$凹性并不是必需的，而且它有排除次指数尾部行为的不幸副作用。在本文中，我们利用最优输运来构造一个形状约束的密度估计量。我们首先使用$\rho-$凹性约束来描述估计量。在此背景下，我们给出了定义估计量的优化问题的相合性、渐近分布和凸性的结果，并对种群密度满足形状约束的零假设进行了检验。然后，利用任意形状约束给出了这些结果成立的充分条件。这一概括被用来探索加州交通部决定授予建筑合同使用第一价格拍卖是否是成本最小化。在Myerson(1981)正则性条件下，我们估计了建筑企业的边际成本，这是第一次价格反向拍卖成本最小化的要求。所提出的测试未能拒绝满足正则性条件。
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英文标题：
《Shape-Constrained Density Estimation via Optimal Transport》
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作者：
Ryan Cumings-Menon
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最新提交年份：
2018
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分类信息：

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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英文摘要：
  Constraining the maximum likelihood density estimator to satisfy a sufficiently strong constraint, $\log-$concavity being a common example, has the effect of restoring consistency without requiring additional parameters. Since many results in economics require densities to satisfy a regularity condition, these estimators are also attractive for the structural estimation of economic models. In all of the examples of regularity conditions provided by Bagnoli and Bergstrom (2005) and Ewerhart (2013), $\log-$concavity is sufficient to ensure that the density satisfies the required conditions. However, in many cases $\log-$concavity is far from necessary, and it has the unfortunate side effect of ruling out sub-exponential tail behavior.   In this paper, we use optimal transport to formulate a shape constrained density estimator. We initially describe the estimator using a $\rho-$concavity constraint. In this setting we provide results on consistency, asymptotic distribution, convexity of the optimization problem defining the estimator, and formulate a test for the null hypothesis that the population density satisfies a shape constraint. Afterward, we provide sufficient conditions for these results to hold using an arbitrary shape constraint. This generalization is used to explore whether the California Department of Transportation's decision to award construction contracts with the use of a first price auction is cost minimizing. We estimate the marginal costs of construction firms subject to Myerson's (1981) regularity condition, which is a requirement for the first price reverse auction to be cost minimizing. The proposed test fails to reject that the regularity condition is satisfied.
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PDF链接：
https://arxiv.org/pdf/1710.09069

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关键词：econometrics Construction Optimization distribution Multivariate 密度 shape 结果 条件 log