Related papers: The Gaussian data assumption does not always lead …
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…
Consider a fading Gaussian MIMO channel with $N_\mathrm{t}$ transmit and $N_\mathrm{r}$ receive antennas. The transmitter selects $L_\mathrm{t}$ antennas corresponding to the strongest channels. For this setup, we study the distribution of…
One-bit quantization has garnered significant attention in recent years for various signal processing and communication applications. Estimating model parameters from one bit quantized data can be challenging, particularly when the…
We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…
The spectrum and statistics of the cosmic microwave background radiation (CMBR) are investigated under the hypothesis that scale invariance of the primordial density fluctuations should be promoted to full conformal invariance. As in the…
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…
Supplement 1 to GUM (GUM-S1) recommends the use of maximum entropy principle (MaxEnt) in determining the probability distribution of a quantity having specified properties, e.g., specified central moments. When we only know the mean value…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
We derive a vector generalization of the curvature-corrected Cram\'er--Rao bound (CRB) in the nonasymptotic regime using a Hilbert space square-root embedding. Building on previous scalar results, we establish a \emph{directional} curvature…
This paper explores as didactically as possible the fundamental principles of both classical and quantum metrology, focusing on the Cram\'er-Rao Bound and how it defines the maximum precision in parameter estimation, taking into account…
Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are…
The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…
We establish bounds on the KL divergence between two multivariate Gaussian distributions in terms of the Hamming distance between the edge sets of the corresponding graphical models. We show that the KL divergence is bounded below by a…
In many practical parameter estimation problems, such as coefficient estimation of polynomial regression, the true model is unknown and thus, a model selection step is performed prior to estimation. The data-based model selection step…
For a given quantum state used in sensing, the quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit on the precision achievable by an unbiased estimator of an unknown parameter, determined by the inverse of the quantum Fisher…
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…
This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of…
Statistical methods are frequently built upon assumptions that limit their applicability to certain problems and conditions. Failure to recognize these limitations can lead to conclusions that may be inaccurate or biased. An example of such…