Non Parametric Estimationa and Testing with Demand Applications

最近有大量关于半参数和非参数估计的理论计量经济学工作，这些估计收敛于或接近参数根N速率。这些估计通常由有限个数的参数在无限大维度干扰参数（非参数分量）存在下的估计组成。目标是对感兴趣的参数进行合理精确的估计和测试，同时最小化或消除任意函数形式的限制。该项目以与实证工作特别相关的方式为计量经济学理论体系做出了贡献。该项目将理论应用于消费者需求分析中的一系列问题。更具体地说，该项目有四个密切相关的部分：1)改进和扩展现有的估计未知函数及其导数在根N速率下的有限维期望的技术；2)构造基于矩的一致性、非参数回归、密度或导数约束的假设检验；3)构造半参数、“无搜索”、根N收敛的多元线性指标模型估计量，该模型既能处理离散回归量，也能处理连续回归量，并能处理包括随机系数在内的一般异方差形式；4)将上述方法应用于Slutsky替代矩阵的非参数估计、同质性和Slutsky对称性的非参数检验、离散或多重有限因变量选择模型的半参数估计以及其他截面需求应用。

There has recently been a great deal of theoretical econometric work in semiparametric and nonparametric estimates that converge at or near parametric, root N rates. These estimators generally consist of estimating as finite number of parameters in the presence of an infinite dimensional nuisance parameter (the nonparametric component). The goal is reasonably precise estimation and testing of parameters of interest while minimizing or eliminating arbitrary function form restrictions. This project contributes to this body of econometric theory in ways that are particularly relevant for empirical work. The project applies the theory empirically to a range of problems in consumer demand analysis. More specifically, the project has four closely interrelated parts: 1) Refining and extending existing techniques of estimating finite dimensional expectations of unknown functions and their derivatives at root N rates; 2) Constructing moment based consistent, nonparametric hypothesis tests of regression, density, or derivative constraints; 3) Constructing a semiparametric, "no search," root N Converging estimator of multiple linear index models that can handle discrete as well as continuous regressors, and can deal with general forms of heteroscedasticity including random coefficients; 4) Applying the above to nonparametric estimation of Slutsky substitution matrices, nonparametric testing of homogeneity and Slutsky symmetry, semiparametric estimation of discrete or multiple limited dependent variable choice models, and other cross sectional demand applications.