Partial identification of probability distributions with misclassified data
误分类数据下概率分布的部分识别AI 解读 ↓
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误分类数据下概率分布的部分识别
- 研究问题
- 离散变量存在误分类、真实分布无法点识别时，如何利用误分类概率的先验信息界定分布及其泛函的识别区域？
- 方法与思路
- 作者以误分类概率矩阵构成线性联立方程，通过对矩阵施加限制纳入先验信息，并提出识别区域估计和置信集方法。
- 材料陈述的贡献
- 摘要称，该方法充分利用先验限制推导真实分布任意实值泛函的识别区域，并以退休计划类型分布作经验说明。
- 阅读关注点
- 应核对误分类矩阵允许的限制、识别区域的刻画是否精确，以及区域估计与置信集如何处理抽样不确定性。
- 阅读边界
- 仅据所给出版社摘要，无法确定先验信息的具体形式、区域宽度或置信集覆盖表现；部分识别也不意味着恢复唯一分布。
原文摘要
This paper addresses the problem of data errors in discrete variables. When data errors occur, the observed variable is a misclassified version of the variable of interest, whose distribution is not identified. Inferential problems caused by data errors have been conceptualized through convolution and mixture models. This paper introduces the direct misclassification approach. The approach is based on the observation that in the presence of classification errors, the relation between the distribution of the 'true' but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations, in which the coefficient matrix is the matrix of misclassification probabilities. Formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities. Such information can have strong identifying power. The direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest. A method for estimating the identification regions and construct their confidence sets is given, and illustrated with an empirical analysis of the distribution of pension plan types using data from the Health and Retirement Study.