Related papers: The Gaussian data assumption does not always lead …
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
In this paper we show how the prediction of CMBR angular power spectra $C_l$ in non-Gaussian theories is affected by a cosmic covariance problem, that is $(C_l,C_{l'})$ correlations impart features on any observed $C_l$ spectrum which are…
By using the $q$-Gaussian distribution derived by the maximum entropy method for spatially-correlated $N$-unit nonextensive systems, we have calculated the generalized Fisher information matrix of $g_{\theta_n \theta_m}$ for $(\theta_1,…
The classical Cram\'er-Rao inequality gives a lower bound for the variance of a unbiased estimator of an unknown parameter, in some statistical model of a random process. In this note we rewrite the statment and proof of the bound using…
Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cram\'er-Rao bound…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
Directed information and its causally conditioned variations are often used to measure causal influences between random processes. In practice, these quantities must be measured from data. Non-asymptotic error bounds for these estimates are…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
Multiple antenna arrays play a key role in wireless networks for communications but also localization and sensing. The use of large antenna arrays pushes towards a propagation regime in which the wavefront is no longer plane but spherical.…
We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A…
Magnetic induction (MI) enables communication in RF-denied environments (underground, underwater, in-body), where the medium conductivity imprints a deterministic signature on the channel. This letter derives a closed-form Cram\'{e}r--Rao…
This paper aims at providing a fresh look at semiparametric estimation theory and, in particular, at the Semiparametric Cram\'{e}r-Rao Bound (SCRB). Semiparametric models are characterized by a finite-dimensional parameter vector of…
Point estimators may not exist, need not be unique, and their distributions are not parameter invariant. Generalized estimators provide distributions that are parameter invariant, unique, and exist when point estimates do not. Comparing…
The attainability of the quantum Cram\'er-Rao bound [QCR], the ultimate limit in the precision of the estimation of a physical parameter, requires the saturation of the quantum information bound [QIB]. This occurs when the Fisher…
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through…
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…
This paper considers the Cram\`er-Rao lower Bound (CRB) for the source localization problem in the near field. More specifically, we use the exact expression of the delay parameter for the CRB derivation and show how this exact CRB can be…
The theoretical foundation of quantum sensing is rooted in the Cram\'er-Rao formalism, which establishes quantitative precision bounds for a given quantum probe. In many practical scenarios, where more than one parameter is unknown, the…
Several current ultra-wide band applications, such as millimeter wave radar and communication systems, require high sampling rates and therefore expensive and energy-hungry analogto-digital converters (ADCs). In applications where cost and…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…