Efficient Inference for Semiparametric and Nonparametric Models

该项目的目标是发展改进的方法，从经济模型和数据中得出结论。所开发的方法应有助于在几个重要应用中作出更准确的误差范围声明。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。应用中实现的自举是一种重采样方法，可以用来提高误差范围计算的准确性。改进的程度取决于如何进行引导。这个项目将考虑最有效的引导可用，并将发展适当的理论。此外，有效自举的重要应用将用于说明潜在的增益。正如本提案将显示的那样，通过使用有效的引导，有很大的改进潜力。(2)半参数模型的有效预测区间和区域。出于预测的目的，计算边际或误差的最有用的方法是通过构建预测区间（和区域）和估计感兴趣的变量落在构建的区间（区域）中的概率。本课题将考虑在给定概率水平的最小长度区间意义上的最优预测区间估计和给定区间长度的最大概率内容的对偶问题。除了这种区间的明显吸引力之外，它们还具有使估计渐近独立于可能具有缓慢收敛速度的讨厌参数估计的附加特征。将最优单变量预测区间方法推广到更相关的最优多元预测区域。(3)具有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差的，由于可能的异方差的附加需求干扰。通过对需求扰动对回归量的依赖关系进行非参数建模，得到了一个独立分量的解决方案。与Hausman-Newey方法不同，Hausman-Newey方法只产生消费者剩余的平均值或中位数，这种方法可以计算消费者剩余的整个分布，然后可以用来开发置信区间，可能是上文提到的最优方式。该方法将从Hausman和Newey的单方程方法扩展到需求方程系统。

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.