Chi-Square Goodness-of-Fit Tests for Randomly Censored Data
随机删失数据的卡方拟合优度检验AI 解读 ↓
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随机删失数据的卡方拟合优度检验
- 研究问题
- 随机删失下，如何利用乘积极限估计得到的单元频数构造拟合优度检验，并评价其局部备择下的渐近效率？
- 方法与思路
- 作者以单元频数的非负定二次型定义广义 Pearson 统计量，允许随机分组和干扰参数估计，并分析渐近分布。
- 材料陈述的贡献
- 摘要称给出原假设与局部备择下的大样本性质；与 Akritas 统计量的效率比较显示，两者不存在统一的支配关系。
- 阅读关注点
- 应核对删失机制、随机分组规则、干扰参数估计条件及二次型选择，并查看效率如何随删失程度和分组数量变化。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；重删失下的优势限于所述 Pitman 效率比较，不能推广为普遍有限样本优势。
原文摘要
We consider general chi-square goodness-of-fit test statistics for randomly censored data--call these generalized Pearson statistics--which are nonnegative definite quadratic forms in the cell frequencies obtained from the product-limit estimator, allowing random cells and general estimators of nuisance parameters. This class of statistics generalizes the class studied by Moore and Spruill in the no censoring case. The large sample behavior of these statistics under the null hypothesis and local alternatives is presented. The chi-square type statistics based on the observed cell frequencies obtained from the product-limit estimator are members of this class for which the quadratic form is selected to produce a chi-square asymptotic null distribution. The generalized Pearson statistic and the statistic by Akritas for a simple hypothesis are compared on the basis of asymptotic relative Pitman efficiency. It is shown that neither statistic dominates the other. The efficiencies are shown to depend on the degree of censoring and the number of cells. For heavily censored data, the Akritas statistic is superior to the generalized Pearson statistic. In the uncensored case, the Akritas statistic, which does not reduce to the Pearson statistic, is not as good as the Pearson statistic in the sense of Pitman efficiency.