Pairwise Difference Estiamtion in Econometrics

本项目研究基于两两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。本研究应该对应用统计学和计量经济学做出有价值的贡献。项目中采用的数据差异方法允许为以前在非参数文献中未考虑到的重要经济模型开发半参数估计器。该方法利用了独立同分布随机变量的差值将在零附近对称分布的事实；通过选择满足该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。对这一问题的研究沿着四条线进行：(1)将现有关于U-过程极小化的结果进行扩展，以允许U-统计量的核依赖于样本大小，就像两两差估计的平滑变体所要求的那样。此外，这些理论结果将被应用于一些潜在的基于半线性、选择和指数模型的成对差分的半参数估计，并且还将考虑成对差分估计的有效构造。(2)对于“平滑”的成对差分估计器，将导出最优带宽的形式，并提出这些最优带宽的“插入式”估计器。(3)发展了依赖于回归函数的初始非参数估计的两两差估计的大样本理论。(4)将使用基于经验的模拟研究对所建议的估计器进行评估。

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.