相关论文: Slepian-Bangs formula and Cramer Rao bound for cir…

We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…

This article proposes a new class of Real Elliptically Skewed (RESK) distributions and associated clustering algorithms that allow for integrating robustness and skewness into a single unified cluster analysis framework. Non-symmetrically…

We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…

We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…

A Cramer-Rao bound (CRB) for semi-blind channel estimators in redundant block transmission systems is derived. The derived CRB is valid for any system adopting a full-rank linear redundant precoder, including the popular cyclic-prefixed…

Elliptically symmetric distributions are a classic example of a semiparametric model where the location vector and the scatter matrix (or a parameterization of them) are the two finite-dimensional parameters of interest, while the density…

Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the…

This work presents a geometric refinement of the classical Cram\'er--Rao bound (CRB) in the non-asymptotic regime by incorporating curvature-aware corrections based on the second fundamental form associated with the statistical model…

We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the…

Primordial non-Gaussianity introduces a scale-dependent variation in the clustering of density peaks corresponding to rare objects. This variation, parametrized by the bias, is investigated on scales where a linear perturbation theory is…

Non-asymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry-Esseen bounds for such approximations with respect to the multivariate…

The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…

This paper extends a recently introduced theory describing particle transport for random statistically homogeneous systems in which the distribution function p(s) for chord lengths between scattering centers is non-exponential. Here, we…

Distributionally robust optimization (DRO) is a powerful framework for training robust models against data distribution shifts. This paper focuses on constrained DRO, which has an explicit characterization of the robustness level. Existing…

In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond…

Tractable generalizations of the Gaussian distribution play an important role for the analysis of high-dimensional data. One very general super-class of Normal distributions is the class of $\nu$-spherical distributions whose random…

We obtain optimal Gaussian concentration bounds (GCBs) for stochastic chains of unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also known as "chains with complete connections" or "$g$-measures". We consider…

This paper derives a general expression for the Cram\'er-Rao bound (CRB) of wireless localization algorithms using range measurements subject to bias corruption. Specifically, the a priori knowledge about which range measurements are…

We consider the distributed compression of Soft Random Geometric Graphs (SRGGs) above the connectivity threshold. We establish the Slepian-Wolf rate region for the SRGG in the setting where there are a finite number of encoders compressing…

We study the derived category of pseudo-coherent complexes over a noetherian commutative ring, building on prior work by Matsui-Takahashi. Our main theorem is a computation of the Balmer spectrum of this category in the case of a discrete…