MAR机制下泊松项目计数技术对敏感问题的研究分析
Analysis of the Sensitivity of the Counting Technology for the Poisson Project under the MAR Mechanism

在对敏感问题进行研究时，出于对隐私的保护，受访者往往拒绝回答或是给出不真实的答案，故现如今敏感问题的研究增益精进，目前十分有效又广泛使用的一种模型为泊松项目计数技术模型，该模型从实验设计上就很好地保护了受访者的隐私以及匿名性，从而引导受访者给出真实有效的答案。然而尽管实验设计有效，在真实调查中，仍然会出现数据缺失的情况，数据缺失分为几种不同情况，分为完全随机缺失，随机缺失和不可忽略的缺失；而由于泊松项目计数技术的实验设计能够保护受访者隐私，因此，假设数据的缺失不是由于受访者害怕泄露隐私而拒绝回答；故本文研究泊松项目计数技术在随机缺失(MAR)下的统计理论推导。经理论计算得，MAR条件下的泊松项目计数技术中，其中的随机缺失数据只依赖于可观测到的数据；故在随机缺失数据下的泊松项目计数技术模型，可以只通过可观测数据进行计算。
When researching sensitive issues, respondents often refuse to answer or give untrue answers due to the protection of privacy, so nowadays, the research on sensitive issues has been improved, and a very effective and widely used model is the Poisson item counting technique model, which protects the privacy and anonymity of the respondents from the experimental design and guides the respondents to give true and effective answers. However, despite the validity of the experimental design, in real surveys, there are still cases of missing data, which are categorized into several different situations, including completely random missing, random missing, and non-negligible missing; since the experimental design of Poisson's item-counting technique protects the privacy of the respondents, it is assumed that the missing data is not due to the fact that respondents are afraid of revealing their privacy and refusing to answer; therefore, this paper investigates the effect of Poisson’s item-counting technique on the random missing (MMS) and the anonymity of the respondents counting technique under missing at random (MAR). After theoretical calculations, the Poisson item counting technique under MAR conditions, in which the random missing data only depends on the observable data; therefore, the model of Poisson item counting technique under random missing data can be calculated only by observable data.