Novel Approaches to Nonlinear Panel Data Analysis and Model Selection

该项目将设计方法来处理在经济和统计建模中经常遇到的不确定性。该项目考虑了以下形式的不确定性：(I)未观察到的变量和(Ii)对模型本身的不完全了解。该项目的第一部分侧重于非线性面板数据模型，它目前在经济和统计建模中受到相当大的关注，因为它们提供了一种自然的方式来描述人口中存在的异质性。这些模型的共同特点是包括了各种未观察到的变量，这些变量代表了随着时间的推移保持不变但因个体而异的因素。该项目将结合熵最大化和基于模拟的估计的思想，在一个统一的框架内处理存在于广泛的非线性面板数据模型中的不可观测变量。所使用的方法旨在绕过在不牺牲解释能力的情况下确定模型的复杂任务。本项目的第二部分提出了一种新的、简单的模型选择方法，该方法依赖于矩估计方法，适合于提供无论候选模型是否重叠都是相同分布的测试。从历史上看，模型选择受到了很大的关注，但往往涉及到首先决定候选模型是否重叠的繁琐步骤--“预测试”。避免预测检验的关键是平滑地在对重叠模型有效的方法和对非重叠模型有效的方法之间进行内插(而不是不连续地切换)。鉴于大量研究人员专注于非线性面板数据模型和模型选择，这些领域的任何新进展都可能引起社会、医学、数学和自然科学几乎所有领域的大型社区的兴趣。最终，该项目将能够在这些领域进行更准确的统计推断，并允许实际使用更一般的统计模型。实施这些方法的计算机程序将公之于众。

This project will devise methods to handle the uncertainty that often is encountered in economic and statistical modeling. The project considers uncertainty taking the form of (i) unobserved variables and (ii) imperfect knowledge of the model itself. The first part of the project focuses on nonlinear panel data models, which currently are receiving considerable attention in economic and statistical modeling because they provide a natural way to describe the heterogeneity present in a population. These models share the feature of including various unobserved variables that represent factors that are constant over time but vary over individuals. The project will combine the ideas of entropy maximization and simulation-based estimation to handle, in a unified framework, the unobservable variables present in a wide range of nonlinear panel data models. The approach used aims to bypass the complex task of establishing identification of the model without sacrificing explanatory power. The second part of this project proposes a new, simple, approach to model selection that relies on method of moments estimation, adapted to deliver tests that are identically distributed whether or not the candidates models are overlapping. Model selection historically has received a lot of attention, but often involves the cumbersome step of "pre-testing" to first decide if the candidate models are overlapping or not. The key to avoiding pre-testing is to smoothly interpolate (rather than discontinuously switch) between a method valid for overlapping models and a method valid for non overlapping models.Given the large number of researchers focusing on nonlinear panel data models and model selection, any new development within these fields is likely to be of interest to a large community in virtually all fields of the social, medical, mathematical, and natural sciences. Ultimately, this project will enable more accurate statistical inference in these fields and permit the practical use of more general statistical models. Computer programs implementing the methods will be made publicly available.