Pairwise Difference Estiamtion in Econometrics

本课题研究了基于两两差分方法的半参数估计量的矩条件或最小化问题的构造和渐近理论。本研究对应用统计学和计量经济学都有重要贡献。项目中采用的数据差分方法允许为非参数文献中以前未考虑过的重要经济模型开发半参数估计。所采用的方法利用了这样一个事实，即独立和同分布的随机变量的差将在零附近对称分布；通过选择满足此条件的观测对的变换，可以构造矩条件来估计感兴趣的参数。关于这个问题的研究沿着四条线进行：(1)关于u过程的最小化的现有结果将得到扩展，以允许u统计量的核依赖于样本量，这是两两差分估计的“平滑”变体所需要的。此外，这些理论结果将应用于一些潜在的半参数估计，基于半线性、选择和指数模型的两两差异，以及两两差异估计的有效构造也将被考虑。(2)对于“平滑”两两差分估计量，将推导出最优带宽的形式，并提出这些最优带宽的“插入”估计量。(3)建立基于回归函数非参数估计的两两差分估计的大样本理论。(4)将使用基于经验的模拟研究来评估所提出的估计器。

This project investigates the construction and asymptotic theory of semiparametric estimators using moment conditions or minimization problems based upon a pairwise differencing approach. This research should make valuable contributions both to applied statistics and econometrics. The data-differencing approach taken in the project permits the development of semiparametric estimators for important economic models that have not previously been considered in the nonparametric literature. The approach taken exploits the fact that the difference of independent and identically-distributed random variables will be symmetrically distributed around zero; by choosing transformations of pairs of observations which satisfy this condition, moment conditions can be constructed to estimate the parameters of interest. The research on this subject proceeds along four lines: (1) Existing results on minimizers of U-processes will be extended to permit the kernel of the U-statistic to depend on the sample size, as required for "smoothed" variants of pairwise difference estimators. Also, these theoretical results will be applied to a number of potential semiparametric estimators, based on pairwise differences for semilinear, selection, and index models, and efficient construction of pairwise difference estimators will also be considered. (2) For the "smoothed" pairwise difference estimators, the form of the optimal bandwiths will be derived, and "plug in" estimators of these optimal bandwidths will be proposed. (3) A large-sample theory for pairwise difference estimators which rely on preliminary nonparametric estimators of regression functions will be developed. (4) The proposed estimators will be evaluated using an empirically-based simulation study.