Adaptive estimation of mixed discrete-continuous distributions under smoothness and sparsity

经济学家经常分析这样的问题，如消费者是否会购买汽车（是或否），如果是这样，花多少钱在汽车上（一个金额，采取任何价值）。 经济学家没有一个很好的方法来分析这些问题。 本研究项目将开发一种新的有效方法来分析具有这些特征的数据。 这些结果将为社会科学研究人员提供一个重要的工具来分析涉及复杂数据结构的问题。 随着日益复杂的数据收集和强大的计算能力的可用性，可以用来有效地分析这样复杂的数据集的方法将是非常有价值的研究人员和决策者在所有领域。 在这项研究中开发的方法将被编程，并免费提供给所有研究人员。 这项研究的结果将使研究人员能够为政策制定者提供更准确的建议，从而改善决策和经济增长。 该研究项目开发了一个用于估计混合离散-连续分布的框架，其中分布的多变量离散部分可以具有大量或少量的支持点;可以是平滑的或不平滑的，并且这些特征可以从一个离散坐标到另一个离散坐标而不同。 离散-连续分布估计的最佳收敛速度将在这些设置中导出。 初步结果表明，平滑是有益的，只有一个子集的离散变量的支持点或足够高的平滑度的数量迅速增长。 建议的估计程序是基于协变量依赖的混合权重的多元正态分布的贝叶斯混合。 所提出的方法将提供实用和最佳的自适应非参数替代标准计量经济模型，如有序概率单位和泊松回归，并在两阶段估计程序的结构离散选择models.This奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Economists often analyze questions such as whether a consumer will buy a car or not (yes or no) and if so how much to spend on the car (an amount that takes any value). Economists do not have a good method to analyze these questions. This research project will develop a new and efficient method to analyze data that has these characteristics. The results will give social science researchers an important tool to analyze problems that involve complicated data structures. With ever increasing sophisticated data collection and the availability of powerful computing power, a method that can be used to efficiently analyze such complicated data sets will be extremely valuable to researchers and policy makers in all fields. The methods developed in this research will be programmed and be freely available to all researchers. The results of this research will allow researchers to give more accurate advice to policy makers and thus improve decision making and economic growth. This research project develops a framework for estimating mixed discrete-continuous distributions where the multivariate discrete part of the distribution can have either a large or a small number of support points; may be smooth or not, and these characteristics can differ from one discrete coordinate to another. The optimal convergence rates for estimation of discrete-continuous distributions will be derived in these settings. Preliminary results suggest that smoothing is beneficial only for a subset of discrete variables with a quickly growing number of support points or sufficiently high level of smoothness. The proposed estimation procedures are based on Bayesian mixtures of multivariate normal distributions with covariate dependent mixing weights. The proposed methods will deliver practical and optimal adaptive nonparametric alternatives to standard econometric models such as ordered probit and Poisson regression, and first stage estimators in two stage estimation procedures for structural discrete choice models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.