两样本枢轴量渐近标准正态性的充要条件
统计理论
2017-10-26 v5 统计理论
摘要
基于来自两个异方差总体的随机样本比较其均值的问题，其渐近解依赖于构造置信区间和检验统计量的枢轴量是否渐近服从标准正态分布。已知若两个样本独立且样本量之比收敛于一个有限正数，则该枢轴量收敛于标准正态分布。我们证明，在不对样本量之比的渐近行为施加任何限制的情况下，样本间相关系数序列的切萨罗收敛到0是该枢轴量收敛的充要条件。我们还得到，在不对样本间相依结构做任何假设的情况下，该枢轴量的两个累次极限均为标准正态分布；并且，若标准化样本均值的联合分布收敛于一个球对称分布，则该分布必定是二元标准正态分布。
引用
@article{arxiv.1612.01668,
title = {Necessary and Sufficient Condition for Asymptotic Standard Normality of the Two Sample Pivot},
author = {Rajeshwari Majumdar and Suman Majumdar},
journal= {arXiv preprint arXiv:1612.01668},
year = {2017}
}
备注
The intended focus of this paper was the asymptotic distribution of the two sample pivot. To obtain that distribution, we had to develop CLT results that ended up constituting about two-thirds of the paper. This caused some dilution of the intended focus and the CLT results got buried. To enhance wider dissemination of the results, we are replacing it by arXiv:1710.07275 and arXiv:1710.08051