Asymptotically Chi-Squared Distributed Tests of Normality for Type II Censored Samples
第二类删失样本的渐近卡方正态性检验AI 解读 ↓
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第二类删失样本的渐近卡方正态性检验
- 研究问题
- 当仅能观测部分次序统计量、形成一般第二类删失样本时，如何检验正态性并获得可用于小样本的临界值近似？
- 方法与思路
- 作者提出三个正态性检验统计量，针对特定备择设计渐近最优性，并通过模拟考察卡方近似与相对检验功效。
- 材料陈述的贡献
- 摘要称，原假设下统计量具有渐近卡方分布；所考察模拟中，样本量为二十五时近似已有用途，功效比较也较有利。
- 阅读关注点
- 应核对删失方案、卡方自由度与正态参数处理、针对备择的最优性定义，以及小样本模拟的具体设置。
- 阅读边界
- 材料为版本未注明的 OpenAlex 索引摘要；具体正则条件与模拟结果未给出，小样本近似和功效评价仅限所考察情形。
原文摘要
A method is proposed for testing normality, in the case of general Type II censored data—that is, data for which only a subset of the order statistics are available. Three test statistics are proposed, which are generalizations of the statistics proposed in LaRiccia (1986), and have many of the same properties. Specifically, they are designed to be asymptotically optimal with respect to specific alternatives and are easily adjusted to be asymptotically optimal with respect to many other types of alternatives. Under the null hypothesis, irrespective of the type or amount of censoring, the proposed test statistics are asymptotically distributed as chi-squared random variables. Further, results of a simulation study are presented, indicating that these statistics converge quite rapidly in distribution to the appropriate chi-squared random variables and that the asymptotic critical values provide a useful approximation to the small sample critical values even for n = 25. The results of a simulation study comparing the power of the proposed tests with some standard tests of normality are presented. These results indicate that, for the cases considered, these statistics compare favorably with the standard procedures.