Related papers: Cramer-Rao Lower Bound and Information Geometry
This paper studies a near-field multiple-input multiple-output (MIMO) radar sensing system, in which the transceivers with massive antennas aim to localize multiple near-field targets in the three-dimensional (3D) space over unknown…
The aim of this paper is to honor Ivo G. Rosenberg by describing some of his most influential results and their impact in logic, discrete mathematics, algebra, and computer science.
In a well-known paper[ARV], Arora, Rao and Vazirani obtained an O(sqrt(log n)) approximation to the Balanced Separator problem and Uniform Sparsest Cut. At the heart of their result is a geometric statement about sets of points that satisfy…
Upper bounds for the $L_p$-discrepancies of point distributions in compact metric measure spaces for $0<p\le\infty$ have been established in the paper [6] by Brandolini, Chen, Colzani, Gigante and Travaglini. In the present paper we show…
This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…
There are many information and divergence measures exist in the literature on information theory and statistics. The most famous among them are Kullback-Leiber's (1951)relative information and Jeffreys (1946) J-divergence, Information…
This article exists first and foremost to contribute to a tribute to Patrick Cattiaux. One of the two authors has known Patrick Cattiaux for a very long time, and owes him a great deal. If we are to illustrate the adage that life is made up…
The algebraic structures known as {\it Leavitt path algebras} were initially developed in 2004 by Ara, Moreno and Pardo, and almost simultaneously (using a different approach) by the author and Aranda Pino. During the intervening decade,…
The cutting-plane approach to integer programming was initiated more that 40 years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner…
We survey recent work on the Cramer-Rao inequality by Hasagawa and Petz; the notion of information manifold in infinite-dimensional Hilbert spaces is introduced, and the extension by Grasselli and the author to quadratic form perturbations…
This paper focuses on three contributions. First, a connection between the result, proposed by Stoica and Babu, and the recent information theoretic results, the worst additive noise lemma and the isoperimetric inequality for entropies, is…
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
Mahlburg (2005) brilliantly showed the importance of crank functions in partition congruences that were originally guessed by Dyson (1944). Ramanujan's partition functions are the centre of these works. Not only for the theory on cranks,…
Finding the optimal attainable precisions in quantum multiparameter metrology is a non trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain…
In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for…
Pranab K. Sen has contributed extensively to many areas of Statistics including order statistics, nonparametrics, robust inference, sequential methods, asymptotics, biostatistics, clinical trials, bioenvironmental studies and…
Computer-based attempts to construct lower bounds for small Ramsey numbers are discussed. A systematic review of cyclic Ramsey graphs is attempted. Many known lower bounds are reproduced. Several new bounds are reported.
Recently, it has been proved in Babadi et al. that in noisy compressed sensing, a joint typical estimator can asymptotically achieve the Cramer-Rao lower bound of the problem.To prove this result, this paper used a lemma,which is provided…
Size-Ramsey numbers are a central notion in combinatorics and have been widely studied since their introduction by Erd\H{o}s, Faudree, Rousseau and Schelp in 1978. Research has mainly focused on the size-Ramsey numbers of $n$-vertex graphs…