Minimax MSE-ratio estimation with signal covariance uncertainties

Robust Linear Estimation with Covariance Uncertainties

We consider the problem of estimating a random vector x, with covariance uncertainties, that is observed through a known linear transformation H and corrupted by additive noise. We first develop the linear estimator that minimizes the worst-case meansquared error (MSE) across all possible covariance matrices. Although the minimax approach has enjoyed widespread use in the design of robust metho...

Minimax Estimation of Large Covariance Matrices 1369

Minimax optimal estimation of general bandable covariance matrices

Cai et al. (2010) [4] have studied the minimax optimal estimation of a collection of large bandable covariance matrices whose off-diagonal entries decay to zero at a polynomial rate. They have shown that the minimax optimal procedures are fundamentally different under Frobenius and spectral norms, regardless of the rate of polynomial decay. To gain more insight into this interesting problem, we...

Minimax Estimation of Large Covariance Matrices under l1-Norm

Driven by a wide range of applications in high-dimensional data analysis, there has been significant recent interest in the estimation of large covariance matrices. In this paper, we consider optimal estimation of a covariance matrix as well as its inverse over several commonly used parameter spaces under the matrix l1 norm. Both minimax lower and upper bounds are derived. The lower bounds are ...

Admissible Minimax Estimation of the Signal with Known Background

Suppose that an observed count X is of the form X = B + S, where the background B and the signal S are independent Poisson random variables with parameters b and θ, b is known, but θ is not. The model arises in astronomy and high-energy physics, and some recent articles have suggested conditioning on the observed bound for B; that is, if X = n is observed, then the suggestion is to base the inf...