Efficient Inference for Semiparametric and Nonparametric Models

点击翻译按钮获取中文摘要

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.