Nonparametric and Semiparametric Inference in Econometric Models

该项目开发了用于计量经济模型估计的非参数和半参数方法。研究包括三个主要部分：1)加性交互回归，2)存在异方差和未知形式自相关的协方差矩阵估计，3)半参数模型中推断的一般方法。相加交互回归(AIR)模型是一种计量经济学模型，它比非参数模型更注重回归函数的结构，从而绕过了严重阻碍完全非参数技术在应用计量经济学中使用的维度问题。这个项目通过分析空气模型的统计特性，并为它们开发有效的估计技术，增加了这项工作。在不同分布假设下协方差矩阵的估计工作通过确定用于这些估计器的合适的带宽/滞后截断参数，并将这些估计器的性质与其他协方差估计器的性质进行比较，扩展了现有关于比较不同核估计器的工作。此外，还发展了计算上有效的估计技术，以获得对任意形式的异方差的一致性。这个项目调查了计量经济学模型中使用的各种估计技术的特性。这些模型被广泛应用于应用经济学的所有领域，包括宏观经济学和政府政策分析、企业和行业行为研究以及国际经济动态。直到最近，所有这些类型的计量经济学研究都是通过假设一个数学函数或函数系统来模拟要检验的经济关系。研究表明，在许多情况下，这些研究的结果可能取决于函数的特定数学规范。在过去十年中，许多计量经济学工作的重点是开发不需要特定数学函数的统计估计技术。这些技术通常被称为非参数技术，与非参数技术相比，它们具有明显的优势，因为必须对经济结构做出更少的假设，而且更多关于经济的信息来自数据本身。然而，使用非参数技术会出现统计问题。这个项目通过研究三个最困难的问题，即维度、协方差估计和计算效率，大大增加了现有的非参数估计工作。

This project develops nonparametric and semiparametric methods for estimation of econometric models. The research consists of three main parts: 1) additive interactive regression, 2) covariance matrix estimation in the presence of heteroskedasticity and autocorrelation of unknown forms, and 3) general methods for inference in semiparametric models. Additive Interactive Regression (AIR) models are econometric models which put more structure on the regression function than nonparametric models, and thus circumvent the problems of dimensionality that severely hinder the use of fully nonparametric techniques in applied econometrics. This project adds to that line of work by analyzing the statistical properties of AIR models, and developing efficient estimation techniques for them. The work on estimation of the covariance matric under varying distributional assumptions extends existing work on comparing different kernel estimators by determining suitable bandwidth/lag truncation parameters for use with these estimators, and comparing the properties of these estimators with those of other covariance estimators. In addition, computationally efficient estimation techniques are developed for obtaining consistency against arbitrary forms of heteroskedasticity. %%% This project investigates the properties of various estimation techniques used in econometric models. Such models are used widely in all areas of applied economics, including macroeconomics and government policy analysis, studies of the behavior of firms and industries, and the dynamics of the international economy. Until recently, all these types of econometric investigations started by postulating a mathematical function or system of functions simulating the economic relationships to be examined. Research has shown that in many cases the results of these studies can be dependent on the particular mathematical specification of the functions. During the last decade much econometric work has focused on developing statistical estimation techniques which do not require a specified mathematical function. These techniques, known generically as nonparametric techniques, have obvious advantages over the nonparametric ones in that fewer assumptions about the structure of the economy have to be made, and more information about the economy is derived from the data themselves. However, statistical problems arise with the use of nonparametric techniques. This project adds significantly to the existing work on nonparametric estimation by examining three of the most difficult problems, namely dimensionality, covariance estimation, and computational efficiency.