Estimation of a high dimensional precision matrix is critical problem to many areas statistics including Gaussian graphical models and inference on data. Working under the structural assumption sparsity, we propose novel methodology for estimating such matrices while controlling false positive rate, percentage entries incorrectly chosen be non-zero. We specifically focus rates tending towards z...

The conditions for the robustness of quantum codes against unreliable measurements are explored: A strict criterion is provided, as well benchmarks and conceptual tools needed building practical devices.

In this paper we evaluate the performance of two reduced resolution filter approaches to data assimilation. The main distinction between these approaches is in the manner they propagate error covariances. Both account for error covariances is a space with dimension m smaller than the model's state vector dimension n. In the first approach the m-dimensional error covariance matrix is interpolate...

High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference the transition matrix under model. While there has been body literature studying sparse estimation matrix, paucity solutions, especially high-dimensional scenario. We develop inferential procedures for...