The stochastic gradient descent (SGD) algorithm is widely used for parameter estimation, especially huge datasets and online learning. While this recursive popular computation memory efficiency, quantifying variability randomness of the solutions has been rarely studied. This article aims at conducting statistical inference SGD-based estimates in an setting. In particular, we propose a fully es...

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 ...