On Estimation under Noisy Order Statistics
On Estimation under Noisy Order Statistics
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DOI：
10.1109/isit.2019.8849813
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
Alex Dytso;Martina Cardone;M. S. Veedu;H. Poor
中科院分区：
文献类型：
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作者：
Alex Dytso;Martina Cardone;M. S. Veedu;H. Poor
本文提出了一个估计框架，用于评估排序函数对扰动数据的性能。具体而言，性能是根据对无扰动的数据计算的排序函数值与使用应用于扰动数据的排序函数的估计值之间的最小均方误差 (MMSE) 来衡量的。首先表明，在实际相关高斯噪声扰动满足的某些条件下，最优估计量可以表示为未排序数据上的估计量的线性组合。然后，提出次优估计器，评估其性能并与最优估计器进行比较。最后，当数据独立同分布时，得出所需 MMSE 的下界。并且服从高斯分布。这是通过解决一个新问题来实现的，该问题包括根据对未排序向量的噪声观察来估计其范数。
This paper presents an estimation framework to assess the performance of the sorting function over data that is perturbed. In particular, the performance is measured in terms of the Minimum Mean Square Error (MMSE) between the values of the sorting function computed on the data without perturbation and the estimate that uses the sorting function applied to the perturbed data. It is first shown that, under certain conditions satisfied by the practically relevant Gaussian noise perturbation, the optimal estimator can be expressed as a linear combination of estimators on the unsorted data. Then, a suboptimal estimator is proposed, and its performance is evaluated and compared to the optimal estimator. Finally, a lower bound on the desired MMSE is derived when data is i.i.d. and has a Gaussian distribution. This is accomplished by solving a new problem that consists of estimating the norm of an unsorted vector from a noisy observation of it.