A Note on the Exact Finite Sample Frequency Functions of Generalized Classical Linear Estimators in Two Leading Over-Identified Cases
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两个典型过度识别情形下广义经典线性估计量的精确有限样本分布
- 研究问题
- 研究联立方程结构系数估计量的精确有限样本分布，以及为什么渐近方差较小不能保证有限样本离散程度也较小。
- 方法与思路
- 作者对题名所指的两个典型过度识别情形开展数学分析，研究广义经典线性估计量的精确有限样本分布及其模拟含义。
- 材料陈述的贡献
- 摘要称报告若干精确分布研究结果，并指出其对计量 Monte Carlo 实验的实施与评价有重要影响，但未列出具体结果。
- 阅读关注点
- 应核对两个过度识别情形的模型与估计量定义、分布的尾部和矩是否存在，以及这些性质如何影响模拟统计量的解释。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，无法确定精确分布形式或估计量排序；数学符号有排版缺失，须查阅原 PDF。
原文摘要
The asymptotic unbiasedness and normality of alternative statistical estimators θ, θ,1 ··· of a given parameter θ* are generally proved without reference to any explicit knowledge of the exact finite sample distribution functions, F n (x), G n (x) ···. (Here n denotes sample size.) Within the class of asymptotically unbiased and normally distributed estimators of a given parameter it is sometimes possible to demonstrate that one estimator possesses a smaller asymptotic variance than another, or that one estimator possesses the smallest asymptotic variance within a particular subclass. Asymptotic theory obviously does not predict anything about finite sample distribution functions Fn(x), Gn(x) ···. In particular we cannot deduce from asymptotic theorems that the estimator with the smallest asymptotic variance will continue to exhibit the smallest dispersion in finite samples. Consequently it remains an essential task in positive estimation theory to derive the exact finite sample distribution functions of the alternative estimators that appear to be promising on the basis of asymptotic considerations. In econometric statistics the alternative estimators of structural coefficients in systems of simultaneous equations appear to possess rather complicated finite sample distribution functions. Monte Carlo experiments are resorted to for the purpose of providing useful leads in mathematical research into the nature of these distributions. In this article are presented some leading results of a mathematical investigation of the exact finite sample distribution functions of generalized classical linear estimators. The results presented here exhibit some particularly important implications for the conduct and evaluation of Monte Carlo experiments in econometric statistics.