Compressed sensing is a very powerful and popular tool for sparse recovery of high dimensional signals. Random sensing matrices are often employed in compressed sensing. In this paper we introduce a new method named aggressive betting using sure independence screening for sparse noiseless signal...

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...

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite ℓ₁-penalized covariance...