Related papers: The Gaussian data assumption does not always lead …

Minimum-variance estimators for the parameter fnl that quantifies local-model non-Gaussianity can be constructed from the cosmic microwave background (CMB) bispectrum (three-point function) and also from the trispectrum (four-point…

Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as…

We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…

The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show…

We consider the problem of distributed estimation of a Gaussian vector with linear observation model. Each sensor makes a scalar noisy observation of the unknown vector, quantizes its observation, maps it to a digitally modulated symbol,…

Meta-backscatter system that utilizes meta-material sensors is a promising enabler for future environmental sensing, offering distinct advantages such as low cost, zero-power consumption, and robustness. Specifically, the electromagnetic…

Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…

The most effective differentially private machine learning algorithms in practice rely on an additional source of purportedly public data. This paradigm is most interesting when the two sources combine to be more than the sum of their…

This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the…

The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…

In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…

Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical…

This paper investigates the asymptotic behavior of the deterministic and stochastic Cram\'er-Rao Bounds (CRB) for semi-blind channel estimation in massive multiple-input multiple-output (MIMO) systems. We derive and analyze mathematically…

We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…

Recently, a widely-used computation expression for quantum Fisher information was shown to be discontinuous at the parameter points where the rank of the parametric density operator changes. The quantum Cram\'er-Rao bound can be violated on…

This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…

In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian…

In this paper, we derive Hybrid, Bayesian and Marginalized Cram\'{e}r-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their…

This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…