Related papers: Cramer-Rao Bound for Arbitrarily Constrained Sets
This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the…
In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims. We analyse bounds for the best position estimation of a stellar-like…
We derive a quantum Cram\'er-Rao bound (QCRB) on the error of estimating a time-changing signal. The QCRB provides a fundamental limit to the performance of general quantum sensors, such as gravitational-wave detectors, force sensors, and…
We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of…
In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cram\'er-Rao bound (CRB) as a performance metric of target estimation, under both point…
In this note an intrinsic version of the Cram\'er-Rao bound on estimation accuracy is established on the Special Orthogonal group $SO(3)$. It is intrinsic in the sense that it does not rely on a specific choice of coordinates on $SO(3)$:…
Precision and accuracy, as two crucial criteria for quantum metrology, have previously lacked rigorous definitions and distinctions. In this paper, we provide a unified definition of precision and accuracy from the perspective of…
In this paper we use the Cramer-Rao lower uncertainty bound to estimate the maximum precision that could be achieved on the joint simultaneous (or 2D) estimation of photometry and astrometry of a point source measured by a linear CCD…
In this paper, we derive for the first time the exact Cramer-Rao bounds (CRBs) on semi-blind channel estimation for amplify-and-forward two-way relay networks. The bounds cover a wide range of modulation schemes that satisfy a certain…
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…
Quantum parameter estimation theory is an important component of quantum information theory and provides the statistical foundation that underpins important topics such as quantum system identification and quantum waveform estimation. When…
We use the Cramer-Rao bound to show which short magnetic reversals can be recovered successfully from a magnetic anomaly profile. Using a simple variant of the Vine-Matthews model, we show, in particular, that errors in determining the…
The paper derives the theoretical Cramer-Rao lower bound for parameter estimation of a source (of emitting energy, gas, aerosol), monitored by a network of sensors providing binary measurements. The theoretical bound is studied in the…
Quantum Cram\'er--Rao theory is intrinsically local: it bounds precision near a specified parameter value, and its saturating measurement generally depends on that value. Barankin-type bounds use finite parameter displacements, but remain…
This paper addresses the real-time state estimation problem for dynamic systems while protecting exogenous inputs against adversaries, who may be honest-but-curious third parties or external eavesdroppers. The Cram\'er-Rao lower bound…
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…
In this paper the problem of assessing bounds on the accuracy of pilot-based estimation of a bandlimited frequency selective communication channel is tackled. Mean square error is taken as a figure of merit in channel estimation and a…
In this study, the hybrid Cramer-Rao bound (CRB) is developed for target localization, to establish the sensitivity of the estimation mean-square error (MSE) to the level of phase synchronization mismatch in coherent Multiple-Input…