A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators
A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators
复制标题
作为计量经济估计量有限样本分布近似的渐近展开理论中的一个一般定理
DOI：
10.2307/1912315
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发表时间：
1977
期刊：
影响因子：
6.1
通讯作者：
P. Phillips
中科院分区：
文献类型：
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作者：
P. Phillips
最近人们对使用 Edgeworth 类型的渐近级数展开来近似计量经济学中的有限样本分布越来越感兴趣。在传统联立方程模型的框架下，许多作者 [1、2、6、7 和 13] 已经导出了各种单方程估计器的此类扩展，并且 Sargan [10] 考虑了开发全信息最大似然估计器 (FIML) 分布扩展的问题。此外，Sargan [11] 最近建立了一个关于统计样本分布的 Edgeworth 展开有效性的重要一般定理，该定理可以表示为样本数据的非常一般的函数，仅对函数类施加弱条件。该结果涵盖了各种计量经济学估计量和检验统计量。然而，迄今为止，该领域的工作基于两个限制性假设：正态分布的结构扰动和非随机外生变量。后者尤其不幸，因为实践中的模型通常涉及回归量集中的滞后变量。另一方面，至少原则上没有理由不能在更一般的模型中获得有效的展开式。因此，本文关注的是扩展[11]中的 Sargan 近似定理以包括此类情况。本文的中心结果在第 2 节中陈述和证明。在第 3 节中，我们对该定理及其条件进行了一些讨论，并尝试将它们与 Sargan 在 [12] 中的同期工作联系起来。
THERE HAS RECENTLY BEEN A GROWING INTEREST in the use of asymptotic series expansions of the Edgeworth type to approximate finite sample distributions in econometrics. Working in the framework of a conventional simultaneous equations model, a number of authors [1, 2, 6, 7, and 13] have derived such expansions for various single-equation estimators and Sargan [10] has considered the problem of developing an expansion of the distribution of the full information maximum likelihood estimator (FIML). In addition, Sargan [11] has recently established an important general theorem on the validity of Edgeworth expansions for sample distributions of statistics which can be represented as very general functions of sample data, imposing only weak conditions on the class of functions. This result covers a wide variety of econometric estimators and test statistics. Nevertheless, work in this field to date has been based on two limiting assumptions: normally distributed structural disturbances and nonrandom exogenous variables. The latter is particularly unfortunate since models in practice usually involve lagged variables in the regressor set. On the other hand, there is no reason in principle, at least, why valid expansions cannot be obtained in more general models. The present paper, therefore, is concerned with extending Sargan's approximation theorem in [11] to include such cases. The central result of the paper is stated and proved in Section 2. In Section 3 we provide some discussion of the theorem and its conditions and attempt to relate them to the contemporaneous work of Sargan in [12].