Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 10,000 papers for “Optimal estimation”

Optimal estimation

KolmanovskiÄ­, V., ShaÄ­khet, L. · Translations of mathematical monographs · 1996

Cited by 0

Optimal Estimation

T. Söderström · Advanced textbooks in control and signal processing · 2002

Cited by 0

Optimal Estimation

Alonzo Kelly · Cambridge University Press eBooks · 2013

Uncertainty is a catch-all term that refers to any and all of the different ways in which the sensors, models, and actuators of a robot do not behave ideally. Sensors rarely give exact and noise-free measurements, environmental models rarely capture all information that matters, and a wheel that does not slip has never been built. As is the case for so many other human capabilities, we rarely notice our own competence dealing with noisy, missing, and conflicting information. This chapter covers some elementary concepts of random processes and then presents classical techniques that can be used to make robots more competent in our uncertain world.

Cited by 1

Optimal Estimation

J. Rissanen · 2013

The first quest for optimal estimation by Fisher, [2], Cramer, Rao and others, [1], dates back to over half a century and has changed remarkably little. The covariance of the estimated parameters was taken as the quality measure of estimators, for which the main result, the Cramer-Rao inequality, sets a lower bound. It is reached by the maximum likelihood (ML) estimator for a restricted subclass of models and asymptotically for a wider class. The covariance, which is just one property of models, is too weak a measure to permit extension to estimation of the number of parameters, which is handled by various ad hoc criteria too numerous to list here. Soon after I had studied Shannon’s formal definition of information in random variables and his other remarkable performance bounds for communication, [4], I wanted to apply them to other fields – in particular to estimation and statistics in general. After all, the central problem in statistics is to extract information from data. After having worked on data compression and introduced arithmetic coding it seemed evident that both estimation and data compression have a common goal: in data compression the shortest code length cannot be achieved without taking advantage of the regular features in data, while in estimation it is these regular features, the underlying mechanism, that we want to learn. This led me to introduce the MDL or Minimum Description Length principle, and I thought that the job was done. However, when starting to prepare this lecture I found that it was difficult, for I could not connect the several in themselves meaningful results to form a nice coherent picture. It was like a jigsaw puzzle where the pieces almost fit but not quite, and, moreover, vital pieces were missing. After considerable struggle I was able to get the pieces to fit but to do so I had to alter them all, and ignore the means and concepts introduced by the masters mentioned above. The result was separation of estimation from data compression, and we can now define optimality for all amounts of data and not just asymptotically. 2

Cited by 0

Optimal Fault Estimation

Henrik Niemann, Ali Saberi, Anton A. Stoorvogel et al. · IFAC Proceedings Volumes · 2000

Cited by 15

Optimal Shrinkage Estimation

S. Ejaz Ahmed, T. Quadir, Sévérien Nkurunziza · International Encyclopedia of Statistical Science · 2025

Cited by 0

Optimal Polyspectra Estimation

J. Fergusson, E. P. S. Shellard · arXiv (Cornell University) · 2011

We show that full inverse covariance weighting can be naturally incorporated into modal estimation methods making them optimal for the CMB power spectrum, bispectrum and trispectrum, as well as in other 3D applications. Modal estimation methods are highly efficient requiring inversion of only an nmax x nmax covariance matrix, where nmax is the limited number of modes needed to describe both the theoretical model and the noise which affects it (in contrast to the full lmax^2 x lmax^2 inverse covariance weighting). A WMAP resolution implementation for modal bispectrum estimation is discussed and shown to yield optimal constraints for local and other models at lmax =500 and nmax <= 50. We also discuss further improvements by characterising and preconditioning the covariance matrix using a single bispectrum variance shape induced by the noise and mask. We describe optimal modal estimation in general terms applicable to polyspectra of any order in a formalism that can be extended beyond the isotropic case. We use the example of anisotropic noise in bispectrum estimation to show the completeness of the isotropic modal basis and the necessity of subtracting a linear estimator term for optimality, removing cross-terms in the variance. We briefly discuss applications to the CMB power spectrum and trispectrum, as well as large-scale structure.

Cited by 9Open access

Optimal Quantum Phase Estimation

U. Dorner, Rafał Demkowicz-Dobrzański, Brian J. Smith et al. · Physical Review Letters · 2009

By using a systematic optimization approach, we determine quantum states of light with definite photon number leading to the best possible precision in optical two-mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit, thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.

Cited by 483Open access

Rate-optimal graphon estimation

Chao Gao, Yu Lu, Harrison H. Zhou · The Annals of Statistics · 2015

Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with $k$ clusters, we show that the optimal rate under the mean squared error is $n^{-1}\log k+k^{2}/n^{2}$. The minimax upper bound improves the existing results in literature through a technique of solving a quadratic equation. When $k\leq\sqrt{n\log n}$, as the number of the cluster $k$ grows, the minimax rate grows slowly with only a logarithmic order $n^{-1}\log k$. A key step to establish the lower bound is to construct a novel subset of the parameter space and then apply Fano’s lemma, from which we see a clear distinction of the nonparametric graphon estimation problem from classical nonparametric regression, due to the lack of identifiability of the order of nodes in exchangeable random graph models. As an immediate application, we consider nonparametric graphon estimation in a Hölder class with smoothness $\alpha$. When the smoothness $\alpha\geq1$, the optimal rate of convergence is $n^{-1}\log n$, independent of $\alpha$, while for $\alpha\in(0,1)$, the rate is $n^{-2\alpha/(\alpha+1)}$, which is, to our surprise, identical to the classical nonparametric rate.

Cited by 205Open access

Optimal estimation of squeezing

Chiribella, G., D'Ariano, G. M., Sacchi, M. F. · arXiv (Cornell University) · 2006

We present the optimal estimation of an unknown squeezing transformation of the radiation field. The optimal estimation is unbiased and is obtained by properly considering the degeneracy of the squeezing operator. For coherent input states, the r.m.s. of the estimation scales as $(2\sqrt {\bar n})^{-1}$ versus the average photon number $\bar n$, while it can be enhanced to $(2\bar n)^{-1}$ by using displaced squeezed states.

Cited by 0Open access

Optimal Bayesian Error Estimation

Lori A. Dalton, Edward R. Dougherty · SPIE eBooks · 2020

Given that a distributional model is needed to achieve useful performance bounds for classifier error estimation when using the training data, a natural course of action is to define a prior distribution over the uncertainty class of feature-label distributions and then find an optimal minimum-mean-squareerror (MMSE) error estimator relative to the uncertainty class (Dalton and Dougherty, 2011b).

Cited by 0

Optimal wave-front estimation

Richard H. Hudgin · Journal of the Optical Society of America · 1977

In a compensated imaging (CI) system the wave-front distortion is changing randomly in time and the data processing must follow the changes and even, to some extent, predict them. Furthermore, the system is not infinitely fast; it has time delays and bandwidth limitations which can be quite significant. Couple to this the substantial photon noise in the wave-front measurements, and it becomes desirable to find the optimal data processing to use for system control. This paper derives the optimal linear control algorithm assuming the aberration and noise statistics are known for a compensated imaging system, and discusses the properties of this algorithm.

Cited by 61