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The mathematical theory of reproducing kernel Hilbert spaces (RKHS) provides powerful tools for minimum variance estimation (MVE) problems. Here, we extend the classical RKHS based analysis of MVE in several directions. We develop a…

Statistics Theory · Mathematics 2013-11-27 Alexander Jung , Sebastian Schmutzhard , Franz Hlawatsch

This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…

Signal Processing · Electrical Eng. & Systems 2018-04-30 Antonio Moschitta , Johan Schoukens , Paolo Carbone

Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…

Quantum Physics · Physics 2025-11-11 Simon K. Yung , Aritra Das , Jun Suzuki , Ping Koy Lam , Jie Zhao , Lorcán O. Conlon , Syed M. Assad

Purpose: To develop a method for optimizing pulsed saturation transfer MR fingerprinting (ST MRF) acquisition. Methods: The Cram\'er-Rao bound (CRB) for variance assessment was employed on Bloch-McConnell-based simulated signals, followed…

Medical Physics · Physics 2025-10-21 Nikita Vladimirov , Moritz Zaiss , Or Perlman

We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…

Quantum Physics · Physics 2015-12-16 Richard Kueng , Christopher Ferrie

In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the…

Machine Learning · Computer Science 2024-05-27 Mingming Ha , Xuewen Tao , Wenfang Lin , Qionxu Ma , Wujiang Xu , Linxun Chen

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

Statistics Theory · Mathematics 2022-11-28 Junichiro Yoshida , Nakahiro Yoshida

Safety-critical navigation applications require that estimation errors be reliably quantified and bounded. This can be challenging for linear dynamic systems if the process noise or measurement errors have uncertain time correlation. In…

Signal Processing · Electrical Eng. & Systems 2020-09-22 Omar Garcia Crespillo , Mathieu Joerger , Steve Langel

Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there…

General Relativity and Quantum Cosmology · Physics 2024-04-02 James W. Gardner , Tuvia Gefen , Simon A. Haine , Joseph J. Hope , Yanbei Chen

A priori bound for the parameter to be estimated is incorporated into confidence intervals within frequentistic approach in a straightforward and optimal fashion, ensuring the best resolution of non-boundary values as well as robustness for…

Data Analysis, Statistics and Probability · Physics 2011-04-06 Fyodor V. Tkachov

Recently, a Wasserstein analogue of the Cramer--Rao inequality has been developed using the Wasserstein information matrix (Otto metric). This inequality provides a lower bound on the Wasserstein variance of an estimator, which quantifies…

Statistics Theory · Mathematics 2025-08-26 Hayato Nishimori , Takeru Matsuda

In this paper, we derive Hybrid, Bayesian and Marginalized Cram\'{e}r-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their…

Machine Learning · Computer Science 2015-06-04 Ranjitha Prasad , Chandra R. Murthy

How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory the variance of an unbiased parameter estimator is bounded from below by the inverse of…

General Relativity and Quantum Cosmology · Physics 2017-10-17 Marcello Rotondo , Yasusada Nambu

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…

Information Theory · Computer Science 2009-10-30 Hana Godrich , Alexander M. Haimovich , H. Vincent Poor

Propagation of error is a widely used estimation tool in experiments, where the estimation precision of the parameter depends on the fluctuation of the physical observable. Thus which observable is chosen will greatly affect the estimation…

Quantum Physics · Physics 2014-10-14 Wei Zhong , Xiao-Ming Lu , Xiaoxing Jing , Xiaoguang Wang

We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…

Statistics Theory · Mathematics 2026-05-28 Diego Martinez-Taboada , Aaditya Ramdas

We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math., October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise"…

Statistics Theory · Mathematics 2017-05-23 Nino Kordzakhia , Yury Kutoyants , Alex Novikov , Lin-Yee Hin

In this letter, we apply previous array receiver architecture which employs time-domain sub-Nyquist sampling techniques to jointly estimate frequency and direction-of-arrival(DOA) of narrowband far-field signals. Herein, a more general…

Information Theory · Computer Science 2018-08-15 Liang Liu , Ping Wei

In parameter estimation, nuisance parameters refer to parameters that are not of interest but nevertheless affect the precision of estimating other parameters of interest. For instance, the strength of noises in a probe can be regarded as a…

Quantum Physics · Physics 2020-12-02 Jun Suzuki , Yuxiang Yang , Masahito Hayashi

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

Machine Learning · Computer Science 2016-09-13 Steve Hanneke