Non Parametric Estimationa and Testing with Demand Applications

最近，在半参数和非参数估计中有大量的理论计量经济学工作，这些估计收敛于或接近参数的根N率。这些估计器通常包括在存在无限维扰动参数(非参数分量)的情况下估计为有限数目的参数。目标是合理精确地估计和测试感兴趣的参数，同时最小化或消除任意函数形式的限制。这个项目以与实证工作特别相关的方式为这套计量经济学理论做出了贡献。该项目将该理论经验地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的N根速率的有限维期望的技术；2)构造回归、密度或导数约束的基于矩的一致性、非参数假设检验；3)构造了多个线性指数模型的半参数、“无搜索”根N收敛估计，它既可以处理离散回归变量，也可以处理连续回归变量，并且可以处理包括随机系数在内的一般形式的异方差；4)将上述结果应用于Slutsky替代矩阵的非参数估计、齐性和Slutsky对称性的非参数检验、离散或多个有限因变量选择模型的半参数估计以及其他横截面需求应用。

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.