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Related papers: Asymptotically Tight Bayesian Cram\'{e}r-Rao Bound

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The constrained Cramer-Rao bound (CCRB) is a lower bound on the mean-squared-error (MSE) of estimators that satisfy some unbiasedness conditions. Although the CCRB unbiasedness conditions are satisfied asymptotically by the constrained…

Information Theory · Computer Science 2019-02-20 Eyal Nitzan , Tirza Routtenberg , Joseph Tabrikian

We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…

Information Theory · Computer Science 2015-06-04 Paul Tune

In constrained parameter estimation, the classical constrained Cramer-Rao bound (CCRB) and the recent Lehmann-unbiased CCRB (LU-CCRB) are lower bounds on the performance of mean-unbiased and Lehmann-unbiased estimators, respectively. Both…

Signal Processing · Electrical Eng. & Systems 2024-10-28 Eyal Nitzan , Tirza Routtenberg , Joseph Tabrikian

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…

Signal Processing · Electrical Eng. & Systems 2025-04-01 Nadav E. Rosenthal , Joseph Tabrikian

-In this paper, we study Bayesian and hybrid Cramer-Rao bounds for the dynamical phase estimation of QAM modulated signals. We present the analytical expressions for the various CRBs. This avoids the calculation of any matrix inversion and…

Information Theory · Computer Science 2015-12-01 Jianxiao Yang , Benoit Geller , A Wei

This paper focusses on the sparse estimation in the situation where both the the sensing matrix and the measurement vector are corrupted by additive Gaussian noises. The performance bound of sparse estimation is analyzed and discussed in…

Information Theory · Computer Science 2015-06-12 Yujie Tang , Laming Chen , Yuantao Gu

Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian…

Machine Learning · Computer Science 2024-06-05 Shion Takeno , Yu Inatsu , Masayuki Karasuyama , Ichiro Takeuchi

In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse…

Statistics Theory · Mathematics 2023-07-19 Mahdi Shaghaghi , Sergiy A. Vorobyov

In [1], we proved the asymptotic achievability of the Cram\'{e}r-Rao bound in the compressive sensing setting in the linear sparsity regime. In the proof, we used an erroneous closed-form expression of $\alpha \sigma^2$ for the genie-aided…

Information Theory · Computer Science 2015-09-16 Behtash Babadi , Nicholas Kalouptsidis , Vahid Tarokh

In this paper, we derive the Cramer-Rao bound (CRB) for joint target position and velocity estimation using an active or passive distributed radar network under more general, and practically occurring, conditions than assumed in previous…

Statistics Theory · Mathematics 2016-04-20 Qian He , Jianbin Hu , Rick S. Blum , Yonggang Wu

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…

Statistics Theory · Mathematics 2026-03-11 Sunder Ram Krishnan

A global network of laser interferometric gravitational wave detectors is projected to be in operation by around the turn of the century. Here, the noisy output of a single instrument is examined. A gravitational wave is assumed to have…

General Relativity and Quantum Cosmology · Physics 2009-10-30 David Nicholson , Alberto Vecchio

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…

Statistics Theory · Mathematics 2026-05-21 Malaak Khatib , Nadav Harel , Joseph Tabrikian , Tirza Routtenberg

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…

Quantum Physics · Physics 2021-03-17 Simon Morelli , Ayaka Usui , Elizabeth Agudelo , Nicolai Friis

Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according…

Methodology · Statistics 2017-07-12 Virginie Ollier , Rémy Boyer , Mohammed Nabil El Korso , Pascal Larzabal

This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…

Quantum Physics · Physics 2020-03-06 Luigi Seveso , Matteo G. A. Paris

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…

Signal Processing · Electrical Eng. & Systems 2025-07-15 Xue Zhang , Abla Kammoun , Mohamed-Slim Alouini

In this paper, we investigate the fundamental limits of MIMO-OFDM integrated sensing and communications (ISAC) systems based on a Bayesian Cram\'er-Rao bound (BCRB) analysis. We derive the BCRB for joint channel parameter estimation and…

Information Theory · Computer Science 2023-08-24 Xinyang Li , Vlad Costin Andrei , Ullrich J Mönich , Holger Boche

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…

Information Theory · Computer Science 2013-08-27 Rad Niazadeh , Masoud Babaie-Zadeh , Christian Jutten

The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has…

Quantum Physics · Physics 2021-02-17 Jasminder S. Sidhu , Yingkai Ouyang , Earl T. Campbell , Pieter Kok