非随机化泊松扰动模型及数据分析  

The Non-randomized Poisson Scrambling Model with Data Analysis

作　　者：刘寅[1] 吴琴[2] LIU Yin;WU Qin(Zhongnan University of Economics and Law,School of Statistics and Mathematics,Wuhan 430073,China;South China Normal University,School of Mathematical Science,Guangzhou 510631,China)

机构地区：[1]中南财经政法大学统计与数学学院,湖北武汉430073 [2]华南师范大学数学科学学院,广东广州510631

出　　处：《数理统计与管理》2021年第6期1051-1068,共18页Journal of Applied Statistics and Management

基　　金：国家自然科学基金(11601524,61773401,11401226)。

摘　　要：为了辅助离散型敏感定量数据的收集,本文提出一种新的非随机响应模型—泊松扰动模型,并给出基于该模型的统计分析方法—包括基于似然函数的统计推断方法以及贝叶斯推断方法.同时,本文提供针对该模型的隐私保护度的评测方法并对非依从行为下非敏感定量变量以及敏感定量变量的均值估计方法进行讨论.最后,通过两个模拟研究以及基于美国南加州一个有关堕胎行为的调查数据的分析来说明本文所提出的方法.To collect the discrete sensitive quantitative data,in this paper,we propose a new noil-randomized response technique,which is called the Poisson scrambling model.Statistical analytical methods including the likelihood-based and the Bayesian approaches are developed.We also discuss the degree of privacy protection for the proposed model and provide the estimation methods for parameters of interest when the non-compliance behavior is taken into consideration.Finally,two simulation studies and an application on survey data about abortion behavior in North California were given to illustrate the proposed techniques.

关 键 词：非随机化响应技术 离散敏感定量数据 零浮动泊松分布 隐私保护度 非依从行为 

分 类 号：C81[社会学—统计学] O212[理学—概率论与数理统计]