Asymptotic Approximations in Semiparametric and Separable Nonparametric Models

9730282林顿，计量经济学在过去15年中取得巨大进步的领域之一是半参数估计。这些新的估计器能够有效地估计广泛的非线性模型的参数，例如Tobit和Probit模型，而关于误差产生过程或任何回归函数的函数形式的信息仅非常少。这笔赠款重申了对半参数估计器的一个主要问题的研究的支持。问题是，这些估计量的渐近分布的一阶近似对于它们在应用经济研究中典型的样本量的抽样行为提供了很差的近似。以前的拨款为一大类参数和半参数估计量和检验统计量的渐近分布发展了更准确的公式。本项目继续这方面的工作：(1)半参数工具变量估计量和检验统计量；(2)半参数二元选择模型；(3)线性回归的自适应估计；(4)参数零相对于非参数替代的规范检验。计算这些估计器通常需要选择一个称为带宽的平滑参数。开发的新扩展提供了二阶最优的带宽选择方法。这笔赠款还提供了绕过维度诅咒的非参数方法，从而提供了灵活但可靠的方法。最基本的模型是加性非参数回归，最近提出了一些新的方法。这笔赠款开发了一种新的方法，似乎解决了以前方法的大部分问题。特别是，它只涉及一维平滑操作，因此完全不受维度诅咒的影响。同时，它是高效的，并且在计算上很容易处理。建立了渐近正态分布。文中将介绍该方法的实际应用效果。该方法将扩展到更一般的模型，允许一些参数分量和更一般类型的可分离性。该项目还调查了可分离性测试。?？

9730282 Linton One of the areas in which econometrics has made great advances during the last fifteen years is semi-parametric estimation. These new classes of estimators are able to efficiently estimate the parameters of a wide array of non-linear models, such as tobit and probit models, with only very minimal information about such things as the error generation process or the function form of any regression functions. This grant renews support for research on a major problem with semi-parametric estimators. The problem is that the first-order approximations to the asymptotic distributions of these estimators provide poor approximations to their sampling behavior for the sample sizes that are typical in applied economic research. The previous grant developed more accurate formulas for the asymptotic distribution of a wide class of parametric and semi-parametric estimators and test statistics. This project continues this work on: (1)semi-parametric instrumental variable estimators and test statistics; (2) semi-parametric binary choice models; (3) adaptive estimation of linear regression; and (4) specification tests of parametric null against non-parametric alternatives. Computing these estimators typically requires selection of a smoothing parameter called the bandwidth. The new expansions developed provide bandwidth selection methods that are second order optimal. This grant also provides non-parametric methods that circumvent the curse of dimensionality and hence provide flexible but reliable methods. The basic model is additive non-parametric regression for which a number of new methods have recently been proposed. This grant develops a new method which seems to resolve most of the problems with previous methods. In particular, it only involves one-dimensional smoothing operations and so is completely free from the curse of dimensionality. At the same time it is efficient and computationally tractable. Asymptotic normality has been established. The practical performanc e of this method will be addressed. The method will be extended to more general models that allow for some parametric components and to more general types of separability. The project also investigators separability tests. ??