Approximations to Finite Sample Moments of Estimators Whose Exact Sampling Distributions are Unknown
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AI 根据所提供的论文材料归类：摘要围绕通用估计量的有限样本矩、随机级数和偏差近似展开，未提供所列领域细分的直接依据。
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精确抽样分布未知时估计量有限样本矩的近似
- 研究问题
- 当结构参数估计量的精确抽样分布未知时，以估计误差展开的前几项近似有限样本矩，能否正确反映偏差的阶数与存在性？
- 方法与思路
- 作者通过例子检验 Nagar 式展开：将估计误差写成按样本量概率阶递减的随机变量级数，并比较截断近似与真实有限样本偏差。
- 材料陈述的贡献
- 摘要称，该近似可产生与真实偏差同阶的误差，还可能把有限偏差与无限偏差判断颠倒，并指出研究随机变量序列时需避免的陷阱。
- 阅读关注点
- 核对反例中真实偏差的计算、级数截断及求期望的条件，重点辨别概率阶展开是否足以保证矩近似与极限运算的有效性。
- 阅读边界
- 摘要未给出反例细节与有效近似的充分条件；文中所称失效针对特定例子，不能据此断言所有 Nagar 式展开或其他矩近似均不可靠。
原文摘要
The exact sampling distributions of estimators of structural parameters of econometric models are unknown except for a few simple cases. In this situation two alternative approaches towards evaluating finite sample properties of various estimators have been adopted in the literature: (i) Monte Carlo experiments, and (ii) the approach pioneered by Nagar and his students in which the sampling error of an estimator is expressed as the sum of an infinite series of random variables, successive terms of which are of decreasing order of sample size in probability. It is claimed that the small sample properties of the estimator under consideration can be approximated by those of the first few terms of such an infinite series. This paper shows through examples that the Nagar approach can be misleading in the sense that it can yield an estimate for finite sample bias that differs from the true finite sample bias to the same order of sample size. And it can yield estimates of bias which are finite (infinite) while the true bias is infinite (finite). The paper also draws attention to some of the pitfalls to be avoided in studying the properties of an infinite sequence of random variables.