Novel Approaches to Nonlinear Panel Data Analysis and Model Selection

该项目将设计方法来处理经济和统计建模中经常遇到的不确定性。 该项目考虑的不确定性采取的形式（一）未观察到的变量和（二）模型本身的不完善的知识。 该项目的第一部分侧重于非线性面板数据模型，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群中存在的异质性。 这些模型的共同特点是包括各种未观察到的变量，这些变量代表随时间变化但随个人变化的因素。 该项目将联合收割机的熵最大化和基于模拟的估计的想法，处理，在一个统一的框架，在广泛的非线性面板数据模型中存在的不可观察的变量。 所使用的方法旨在绕过在不牺牲解释力的情况下确定模型的复杂任务。 该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，适用于提供相同分布的测试，无论候选模型是否重叠。 模型选择在历史上受到了很多关注，但通常涉及繁琐的“预测试”步骤，首先决定候选模型是否重叠。 避免预测试的关键是平滑插值（而不是不连续地切换）重叠模型有效的方法和非重叠模型有效的方法。鉴于大量的研究人员专注于非线性面板数据模型和模型选择，这些领域内的任何新发展都可能引起社会，医学，数学，和自然科学。 最终，该项目将使这些领域的统计推断更加准确，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开提供。

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.