零浮动Poisson项目计数法在敏感数据抽样调查中的应用

Application of Zero-inflated Poisson Item Count Technique for Sample Surveys With Sensitive Data

文章将Poisson-Poisson项目计数法进行推广,提出零浮动Poisson项目计数法,其中,非敏感辅助变量来自于一个参数已知的零浮动Poisson分布。并给出了该模型下敏感参数极大似然估计的EM算法以及构造其置信区间的bootstrap方法。此外,还对该模型保护受访者隐私的能力加以讨论,发现该模型的隐私保护要优于Poisson-Poisson项目计数法。最后,从随机模拟的结果表明在该模型下利用本文所介绍的分析方法可以得到敏感参数的较为准确的估计。

This paper extends the Poisson-Poisson item count technique to the zero-inflated Poisson item count technique,where the non-sensitive auxiliary variable comes from a zero-inflated Poisson distribution with known parameters.The paper also provides the EM algorithm to calculate the maximum likelihood estimate for the sensitive parameter as well as the bootstrap method in constructing confidence intervals.Furthermore,the paper discusses the ability of privacy protection of the proposed model and finds out that it performs better than that of the Poisson-Poisson item count approach.Finally,the results of the stochastic simulation show that a more accurate estimate of the sensitive parameters can be obtained by using the analytical method described in the paper.