All norms in this section are defined elementwise. To recap, we solve the following problem: The Lagrangian of (1) is

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension p is large. Gaussian graphical models provide an important tool in describing conditional independence through presence or absence of the edges in the underlying graph. A popular non-Bayesian method of estimating a graphical structure is given by the gr...

We consider the problem of estimating sparse precision matrix of Gaussian copula distributions using samples with missing values in high dimensions. Existing approaches, primarily designed for Gaussian distributions, suggest using plugin estimators by disregarding the missing values. In this paper, we propose double plugin Gaussian (DoPinG) copula estimators to estimate the sparse precision mat...

We consider the estimation of noise parameters in a quantum channel, assuming the most general strategy allowed by quantum mechanics. This is based on the exploitation of unlimited entanglement and arbitrary quantum operations, so that the channel inputs may be interactively updated. In this general scenario, we draw a novel connection between quantum metrology and teleportation. In fact, for a...

We propose a semiparametric method for estimating sparse precision matrix of high dimensional elliptical distribution. The proposed method calibrates regularizations when estimating each column of the precision matrix. Thus it not only is asymptotically tuning free, but also achieves an improved finite sample performance. Theoretically, we prove that the proposed method achieves the parametric ...

In the context of multiconjugate adaptive optics, the optimum linear estimation of a wave-front phase for a target object using the phases of several surrounding natural guide stars (NGS’s) is studied. A Wiener-filtertype estimator is constructed. The minimum residual wave-front-phase (tomographic) error depends on the turbulence vertical profile, and for typical profiles it is almost insensiti...

Whereas probabilistic calibration has been a central normative concept of accuracy in previous research on interval estimates, we suggest here that normative approaches for the evaluation of judgmental estimates should consider the communicative interaction between the individuals who produce the judgments and those who receive or use them for making decisions. We analyze precision and error in...