基于差分隐私度序列的Thurstone模型中参数估计量的渐近性理论

Asymptotic theory of parameter estimators in Thurstone model based on differential privacy sequence

Thurstone模型主要用于研究成对数据比较问题的统计模型,该模型在心理测量、社交选择、推荐系统等方面有着广泛的应用.然而,由于心理学研究中常常获取包含着个人隐私的数据,直接将数据发布进行分析会带来隐私泄露的风险.为解决数据隐私泄露问题,通过对原始数据加入离散Laplace噪声进行加密,然后利用数理统计方法建立了带有噪声的Thurstone模型参数的渐近性理论.最后通过数值模拟验证了理论结果.

Thurstone model is a statistical model mainly used to study the comparison of paired data,it is widely used in psychological measurement,social choice,recommendation system and so on However,because psychological research often obtains data containing personal privacy,publishing and analyzing the data directly will bring the risk of privacy disclosure.In order to solve the problem of data privacy disclosure,this paper encrypts the original data by adding discrete Laplace noise,and then establishes the asymptotic theory of the parameters of Thurstone model with noise by using the method of mathematical statistics Finally,the theoretical results are verified by numerical simulation.