Technical Program

Paper Detail

Paper Title On Estimation under Noisy Order Statistics
Paper IdentifierMO1.R3.1
Authors Alex Dytso, Princeton University, United States; Martina Cardone, Mishfad S. Veedu, University of Minnesota, United States; H. Vincent Poor, Princeton University, United States
Session Estimation I
Location Monge, Level 3
Session Time Monday, 08 July, 09:50 - 11:10
Presentation Time Monday, 08 July, 09:50 - 10:10
Manuscript  Click here to download the manuscript
Abstract his 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.