Pairwise Difference Estiamtion in Econometrics

本计画研究构造与渐近理论 使用矩条件的半参数估计，或 最小化问题的基础上成对差分方法。 这项研究将为应用 统计学和计量经济学。 采用的数据差异方法 在该项目允许半参数估计的发展 对于重要的经济模型， 在非参数文献中考虑。 采取的办法 利用了这样一个事实， 相同分布的随机变量将对称 分布在零附近;通过选择 满足这个条件的观测，矩条件可以 来估计感兴趣的参数。 关于这个问题的研究沿着四条路线进行： (1)推广了U-过程极小元的已有结果 允许U统计量的核依赖于样本 大小，如成对差异的“平滑”变体所需 估计器。 此外，这些理论结果将被应用到一个 潜在半参数估计量的数量，基于成对 半线性、选择和指数模型的差异，以及 两两差异估计的有效构造也将 被考虑。 (2)对于“平滑”成对差分估计量， 的最佳带宽将被导出，和“插入”估计 将提出这些最佳带宽。 (3)两两差分估计量的大样本理论， 依赖于回归的初步非参数估计 将开发功能。 (4)建议的估计量将使用 基于计算机的模拟研究。

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.