Pairwise Difference Estiamtion in Econometrics

该项目研究使用基于成对差分方法的矩条件或最小化问题的半参数估计量的构造和渐近理论。 这项研究应该对应用统计学和计量经济学做出宝贵的贡献。 该项目中采用的数据差分方法允许为重要的经济模型开发半参数估计器，这些模型以前在非参数文献中尚未考虑过。 所采用的方法利用了这样一个事实：独立且同分布的随机变量的差异将对称分布在零附近；通过选择满足该条件的观测对的变换，可以构建矩条件来估计感兴趣的参数。 关于这个主题的研究沿着四个方向进行：（1）U 过程最小化器的现有结果将被扩展，以允许 U 统计的内核依赖于样本大小，正如成对差分估计量的“平滑”变体所需要的那样。 此外，这些理论结果将基于半线性、选择和指数模型的成对差异应用于许多潜在的半参数估计器，并且还将考虑成对差异估计器的有效构造。 (2)对于“平滑的”成对差分估计器，将导出最佳带宽的形式，并且将提出这些最佳带宽的“插入”估计器。 (3) 将开发依赖于回归函数的初步非参数估计器的成对差分估计器的大样本理论。 (4) 将使用基于经验的模拟研究来评估所提出的估计量。

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.