标题： 有缺陷计数数据的推断：二项卷积框架下的估计 显示英文标题

标题： Inference for Error-Prone Count Data: Estimation under a Binomial Convolution Framework

摘要： 计数数据中的测量误差很常见，但在文献中研究不足，特别是在观察到的分数有界且来自离散评分过程的背景下。 受口腔阅读流利度评估应用的启发，我们提出了一种二项卷积框架，该框架将二元错误分类模型扩展到仅观察到正确响应总数的设置中，并且误差可能涉及对事件数量的高估和低估。 该模型能够适应不同的真正阳性准确率和真正阴性准确率，并保持数据的有界性质。 假设在部分项目上可以获得污染和无误差的分数，我们开发并比较了三种估计策略：最大似然估计（MLE）、线性回归和广义矩方法（GMM）。 大量模拟结果显示，当模型正确指定时，MLE最为准确，但计算量大且对模型误设不稳健。 回归方法简单且稳定，但精度较低，而GMM在模型依赖性方面提供了折中方案，尽管它对异常值敏感。 在实践中，该框架支持在无监督设置中的改进推断，其中污染分数作为下游分析的输入。 通过量化准确率，即使尚未定义特定结果，该模型也能实现分数校正。 我们使用真实的口腔阅读流利度数据演示了其效用，并比较了人工和AI生成的分数。 研究结果突显了估计器选择的实际意义，并强调了在计数数据中明确建模不对称测量误差的重要性。 显示英文摘要

摘要： Measurement error in count data is common but underexplored in the literature, particularly in contexts where observed scores are bounded and arise from discrete scoring processes. Motivated by applications in oral reading fluency assessment, we propose a binomial convolution framework that extends binary misclassification models to settings where only the aggregate number of correct responses is observed, and errors may involve both overcounting and undercounting the number of events. The model accommodates distinct true positive and true negative accuracy rates and preserves the bounded nature of the data. Assuming the availability of both contaminated and error-free scores on a subset of items, we develop and compare three estimation strategies: maximum likelihood estimation (MLE), linear regression, and generalized method of moments (GMM). Extensive simulations show that MLE is most accurate when the model is correctly specified but is computationally intensive and less robust to misspecification. Regression is simple and stable but less precise, while GMM offers a compromise in model dependence, though it is sensitive to outliers. In practice, this framework supports improved inference in unsupervised settings where contaminated scores serve as inputs to downstream analyses. By quantifying accuracy rates, the model enables score corrections even when no specific outcome is yet defined. We demonstrate its utility using real oral reading fluency data, comparing human and AI-generated scores. Findings highlight the practical implications of estimator choice and underscore the importance of explicitly modeling asymmetric measurement error in count data.