Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny, Berlin, Germany, November 6-8, 2019, Moscow, Russia, November 30, 2019
Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny, Berlin, Germany, November 6-8, 2019, Moscow, Russia, November 30, 2019
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现代统计基础 - 纪念弗拉基米尔·斯波科尼 (Vladimir Spokoiny) 的庆典，德国柏林，2019 年 11 月 6-8 日，俄罗斯莫斯科，2019 年 11 月 30 日
DOI：
10.1007/978-3-031-30114-8_2
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Dubois A
中科院分区：
文献类型：
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作者：
Dubois A
我们解决的问题的拟合优度测试Hölder连续密度下的局部差分隐私约束。我们研究极小极大分离率时，只有非交互式的隐私机制被允许使用，当非交互式和顺序交互式可用于私有化。我们提出了隐私机制和相关的测试程序，其分析使我们能够获得上界的极大极小率。这些结果是补充下界。通过比较这些界限，我们表明，建议的隐私机制和测试是最佳的，最多的对数因子的几个选择ofincluding密度从均匀，正常，Beta，柯西，帕累托，指数分布。特别是，我们观察到的结果是恶化的私人设置相比，非私人的。此外，我们表明，顺序交互机制改善时，只考虑非交互式隐私机制所获得的结果。
We address the problem of goodness-of-fit testing for Hölder continuous densities under local differential privacy constraints. We study minimax separation rates when only non-interactive privacy mechanisms are allowed to be used and when both non-interactive and sequentially interactive can be used for privatisation. We propose privacy mechanisms and associated testing procedures whose analysis enables us to obtain upper bounds on the minimax rates. These results are complemented with lower bounds. By comparing these bounds, we show that the proposed privacy mechanisms and tests are optimal up to at most a logarithmic factor for several choices ofincluding densities from uniform, normal, Beta, Cauchy, Pareto, exponential distributions. In particular, we observe that the results are deteriorated in the private setting compared to the non-private one. Moreover, we show that sequentially interactive mechanisms improve upon the results obtained when considering only non-interactive privacy mechanisms.