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We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

Statistics Theory · Mathematics 2024-03-05 Rémy Degenne , Timothée Mathieu

The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…

Computation · Statistics 2016-02-17 Omri Har Shemesh , Rick Quax , Borja Miñano , Alfons G. Hoekstra , Peter M. A. Sloot

Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…

Quantum Physics · Physics 2012-09-04 Xiao-Ming Lu , Shunlong Luo , C. H. Oh

We consider the problem of distributed estimation of a Gaussian vector with linear observation model. Each sensor makes a scalar noisy observation of the unknown vector, quantizes its observation, maps it to a digitally modulated symbol,…

Information Theory · Computer Science 2020-05-01 Mojtaba Shirazi , Azadeh Vosoughi

Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…

Statistical Mechanics · Physics 2026-01-21 Pedro B. Melo , Sílvio M. Duarte Queirós , Diogo O. Soares-Pinto , Welles A. M. Morgado

This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for…

Statistics Theory · Mathematics 2021-07-01 Juan Carlos Escanciano

We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is…

Statistical Mechanics · Physics 2023-09-06 Joseph A. Smiga , Marco Radaelli , Felix C. Binder , Gabriel T. Landi

In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the…

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…

Probability · Mathematics 2024-08-20 Nguyen Tien Dung , Nguyen Thu Hang

The concept of Fisher information can be useful even in cases where the probability distributions of interest are not absolutely continuous with respect to the natural reference measure on the underlying space. Practical examples where this…

Statistics Theory · Mathematics 2018-03-28 Jeremie Houssineau , Ajay Jasra , Sumeetpal S. Singh

In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…

Statistics Theory · Mathematics 2017-10-18 Alexander Ly , Maarten Marsman , Josine Verhagen , Raoul Grasman , Eric-Jan Wagenmakers

We introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems. In particular we generalize an orthonormality relation…

Statistical Mechanics · Physics 2014-09-16 Matteo Polettini

Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…

Machine Learning · Computer Science 2022-12-20 Ibrahim Alsolami , Tomoki Fukai

We derive a connection between performance of estimators the performance of the ideal observer on related detection tasks. Specifically we show how Shannon Information for the task of detecting a change in a parameter is related to the…

Information Theory · Computer Science 2019-07-24 Eric Clarkson

We consider the problem of learning high-dimensional, nonparametric and structured (e.g. Gaussian) distributions in distributed networks, where each node in the network observes an independent sample from the underlying distribution and can…

Information Theory · Computer Science 2019-06-04 Leighton Pate Barnes , Yanjun Han , Ayfer Ozgur

The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…

Statistics Theory · Mathematics 2021-09-24 Antony M. Overstall

Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a…

Data Analysis, Statistics and Probability · Physics 2009-03-22 S. Prasad , N. C. Menicucci

Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…

Classical Physics · Physics 2023-10-06 Mohamed Sahbani , Swetamber Das , Jason R. Green

The speed at which one can minimize an expected loss using stochastic methods depends on two properties: the curvature of the loss and the variance of the gradients. While most previous works focus on one or the other of these properties,…

Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…

Quantum Physics · Physics 2009-11-07 Denes Petz