估计噪声阶次统计量
Estimating Noisy Order Statistics
摘要：
本文提出了一种估计框架，以评估在扰动/噪声数据排序的性能。特别是，恢复精度测量的最小均方误差（MMSE）之间的排序函数的值计算的数据没有扰动和估计器上的排序噪声数据。它首先表明，在一定的对称性条件下，满足例如由实际相关的高斯噪声扰动，最佳估计可以表示为一个线性组合的未排序数据的估计。然后，提出了两个次优估计和性能保证，他们的最优估计。最后，一些令人惊讶的性能的MMSE的兴趣被发现。例如，它示出的MMSE增长与数据大小呈次线性，并且常用的MMSE下限，如贝叶斯Cramér-Rao和最大熵界要么不能应用或不合适。
英文摘要：
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting function computed on data without perturbation and the estimator that operates on the sorted noisy data. It is first shown that, under certain symmetry conditions, satisfied for example by the practically relevant Gaussian noise perturbation, the optimal estimator can be expressed as a linear combination of estimators on the unsorted data. Then, two suboptimal estimators are proposed and performance guarantees on them are derived with respect to the optimal estimator. Finally, some surprising properties on the MMSE of interest are discovered. For instance, it is shown that the MMSE grows sublinearly with the data size, and that commonly used MMSE lower bounds such as the Bayesian Cramér-Rao and the maximum entropy bounds either cannot be applied or are not suitable.
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