AI 中文总结
研究如何用雷尼散度测度检测有偏样本，提出针对未删失和I型删失数据的统计检验方法，通过模拟得临界值，经功效研究与其他检验比较，并分析真实数据集，展示该方法检测长度偏差实用价值。
AI 中文摘要
加权分布出现在观测值以不等概率选取或某些事件不可观测的情况下。检测这种抽样偏差对于确保有效的统计推断至关重要。本文提出一种使用雷尼散度测度检测样本偏差的统计检验方法。该检验统计量针对未删失和I型删失数据构建，具有包括渐近正态性等理论性质。通过在威布尔分布下针对一系列样本量和删失比例进行模拟得到临界值。进行全面的功效研究将该检验与现有基于库尔贝克-莱布勒散度的检验和似然比检验进行比较。分析两个真实数据集以证明该检验在检测长度偏差方面的实际效用。
英文摘要
Weighted distributions arise in situations where observations are selected with unequal probabilities or because of the non-observability of some events. Detecting such sampling bias is essential for ensuring valid statistical inference. In this paper, we propose a statistical test for detecting bias in a sample using the Renyi divergence measure. The proposed test statistic is formulated for both uncensored and type-I censored data and possesses several theoretical properties including asymptotic normality. Critical values are obtained through simulations under the Weibull distribution for a range of sample sizes and censoring proportions. A comprehensive power study compares the proposed test with the existing Kullback-Leibler divergence-based test and the likelihood ratio test. Two real datasets are analyzed to demonstrate the practical utility of the proposed test in detecting length bias.
