Asymptotic Approximations in Parametric and Semiparametric Models

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。这些新类型的估计器能够有效地估计各种非线性模型的参数，例如tobit和probit模型，只需要非常少的关于诸如误差生成过程或任何回归函数的函数形式的信息。这些估计量的一个问题是，对这些估计量的渐近分布的一阶近似值对应用经济研究中典型的样本量的抽样行为提供了较差的近似值。本研究为广泛的参数和半参数估计量及检验统计量的渐近分布发展了更精确的公式。有三个项目。第一个项目继续了主要研究者关于半参数模型渐近分布的二阶近似的工作。计算这些估计量通常需要选择一个平滑参数，称为带宽。根据这项拨款开发的新扩展提供了二阶最优的带宽选择方法。第二个项目发展参数ARCH时间序列模型的估计量和检验统计量的渐近展开式。然后，这些新的扩展用于提供偏差和大小校正程序，并在这些复杂的程序中评估小样本效应的大小。它们还提供更精确的抽样分布的小样本近似值。第三项研究了一类新的半参数持续时间数据模型，并推导了它们的一阶渐近理论。

SBR-9423102 Oliver 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 functional form of any regression functions. One problem with these estimators is that 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. This research develops more accurate formulas for the asymptotic distribution of a wide class of parametric and semi-parametric estimators and test statistics. There are three projects. The first project continues the principals investigator's work on second-order approximations of the asymptotic distribution of semi-parametric models. Computing these estimators typically requires the selection of a smoothing parameter, called the bandwidth. The new expansions developed under this grant provide bandwidth selection methods that are second order optimal. The second project develops asymptotic expansions for estimator and test statistics of parametric ARCH time series models. These new expansions are then used to provide bias and size correction procedures and to evaluate the magnitude of small sample effects in these complicated procedures. They also provide more accurate small sample approximations of the sampling distribution. The third project investigates a new class of semiparametric models for duration data and derives their first-order asymptotic theory.