相关论文: A geometer's view of the the Cram\'er-Rao bound on…

We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…

The quantity of interest in the classical Cram\'er-Rao theory of unbiased estimation (e.g., the Cram\'er-Rao lower bound, its exact attainment for exponential families, and asymptotic efficiency of maximum likelihood estimation) is the…

The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing…

A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…

The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…

The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…

Many results in the quantum metrology literature use the Cram\'er-Rao bound and the Fisher information to compare different quantum estimation strategies. However, there are several assumptions that go into the construction of these tools,…

In his 2005 paper, S.T. Smith proposed an intrinsic Cram\'er-Rao bound on the variance of estimators of a parameter defined on a Riemannian manifold. In the present technical note, we consider the special case where the parameter lives in a…

A general class of Bayesian lower bounds when the underlying loss function is a Bregman divergence is demonstrated. This class can be considered as an extension of the Weinstein--Weiss family of bounds for the mean squared error and relies…

The widely used quantum Cramer-Rao bound (QCRB) sets a lower bound for the mean square error of unbiased estimators in quantum parameter estimation, however, in general QCRB is only tight in the asymptotical limit. With a limited number of…

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…

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…

In this lecture note, we show a general property of the Cramer-Rao bound (CRB) that quantifies the interdependencies between the parameters in a vector. The presented result is valid for more general models than the additive noise model and…

A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…

The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable…

The best possible precision is one of the key figures in metrology, but this is established by the exact response of the detection apparatus, which is often unknown. There exist techniques for detector characterisation, that have been…

This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup,…

This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…

We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…

The relative $\alpha$-entropy is the R\'enyi analog of relative entropy and arises prominently in information-theoretic problems. Recent information geometric investigations on this quantity have enabled the generalization of the…