Efficient Inference for Semiparametric and Nonparametric Models

该项目的目标是制定更好的方法，从经济模型和数据中得出推论。所开发的方法应有助于在几个重要的应用中做出更准确的误差幅度声明。该项目包括三个具体的项目和扩展：（1）半参数模型的有效自举。自举，如在应用中实现的，是一种可用于提高误差容限计算的准确性的恢复方法。改进的程度可以取决于如何进行自举。该项目将考虑最有效的引导，并将开发适当的理论。此外，有效的引导的重要应用将被用来说明潜在的增益。正如本提案所示，通过使用高效的引导程序，有很大的改进潜力。(2)半参数模型中的有效预测区间和区域。为了预测的目的，计算裕度或误差的最有用的方法是通过构建预测区间（和区域）以及估计感兴趣的变量落在构建的区间（区域）中的概率。本项目将考虑最佳预测区间的估计在给定概率水平的最小长度区间和给定区间长度的最大概率内容的对偶问题。除了明显的吸引力，这样的间隔，他们有额外的功能，使估计渐近独立的滋扰参数估计，可能有缓慢的收敛速度。最优单变量预测区间方法将扩展到更相关的最优多变量预测区域。(3)带非加性误差的非参数和半参数回归。该项目表明，半参数消费者剩余计算是有偏见的，由于可能异方差的附加需求扰动。提出了一种解决方案，通过非参数化建模的依赖回归的需求扰动的一个独立的组件。与只能得出平均或中位数消费者剩余的豪斯曼-纽维方法不同，这种方法能够计算消费者剩余的整个分布，然后可以用于开发置信区间，可能是上述方式的最佳选择。这种方法将从豪斯曼和纽维的单一方程方法扩展到尽可能多的需求方程系统。

The objective of this project is to develop improved methods for drawing inference from economic models and data. The methods developed should help to make more accurate margin of error statements in several important applications. The project includes three specific projects and extensions:(1) Efficient bootstrapping in semiparametric models. Bootstrapping, as implemented in application, is a resampling method that can be used to improve the accuracy of margin of error calculations. The degree of improvement can depend on how the bootstrapping is done. This project will consider the most efficient bootstrap available and will develop appropriate theory. Also important applications of the efficient bootstrap will be used to illustrate the potential gain. As this proposal will show, there is large potential for improvements through the use of an efficient bootstrap. (2) Efficient prediction intervals and regions in semiparametric models. For prediction purposes, the most useful approach to calculation of margins or error is through the construction of predictive intervals (and regions) and the estimation of the probability of the variable(s) of interest falling in the constructed interval (region.) This project will consider the estimation of optimal predictive intervals in the sense of minimum length intervals given the probability level and the dual problem of maximum probability content given the interval length. Aside from the obvious attraction of such intervals they have the added feature of rendering the estimates asymptotically independent of nuisance parameters estimators that might have slow rates of convergence. The optimal univariate predictive interval approach will be extended to the more relevant optimal multivariate predictive region.(3) Nonparametric and semiparametric regression with nonadditive errors. The project shows that semiparametric consumer surplus calculations are biased due to likely heteroskedasticity of the additive demand disturbances. A solution is proposed by nonparametrically modeling the dependence of the demand disturbances on the regressors up to an independent component. Unlike the Hausman-Newey approach which only yields the mean or median consumer surplus, this approach enables the calculation of the entire distribution of the consumer surplus, which can then be used to develop confidence intervals, possibly optimal in the fashion mentioned above. The approach will be extended from the single equation approach of Hausman and Newey to systems of demand equations to the extent possible.