Statistical estimation of measure invariants

Timofeev, E. A.

doi:10.1090/s1061-0022-06-00919-8

Cited by 14 publications

(6 citation statements)

References 34 publications

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“…2) made it possible to increase the electromagnetic force by 3 times, the power density by 30%, and reach a power of 100 W to 100 kW. At the same time, a greater torque of up to 15 Nm was provided at a rotation speed of 1500 rpm [3,8,11,14].…”

Section: Objects and Methods Of Researchmentioning

confidence: 99%

Methods of new technological developments of electric motors based on soft magnetic materials

Berdiev,

Kolesnikov,

Tuychieva

et al. 2023

E3S Web of Conf.

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Application conditions of composite materials based on ASC100.29 iron powders with an oxide coating in electrical machine devices as a stator with improved performance are considered in the article. The conditions for increasing the stability of the operation of electric motors are determined based on changes in the thickness of the oxide layer. Three-dimensional models of magnetic circuits were used, which made it possible to achieve a force of up to 4500 N with a torque of 3 to 8 Nm, which made it possible to obtain an engine power of 100-200 W. As a result, experimental characteristics of dependences μ=f(h), H=f(h)) and the power of specific losses on the thickness of the oxide coating ωyд=f(h) were obtained. Methods for measuring the dynamic characteristics of the stator magnetic circuit are determined.

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Section: Objects and Methods Of Researchmentioning

confidence: 99%

Methods of new technological developments of electric motors based on soft magnetic materials

Berdiev,

Kolesnikov,

Tuychieva

et al. 2023

E3S Web of Conf.

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“…For estimator r (k,m) n (ρ)/ log n, L 1 -convergence and variance bound O(n −c ) are shown [11] under certain restriction on source measures. For metric 3 specifically, this measure restriction is relaxed (see 8) and convergence almost everywhere is established in [6].…”

Section: Evgeniy Timofeev and Alexei Kaltchenkomentioning

confidence: 98%

“…We point out that it is often more convenient to estimate, instead of the entropy, its inverse quantity 1/h. Two modifications of a Grassberger's estimator [5] are proposed in [11]. In this paper notation, they are written as r…”

Section: Evgeniy Timofeev and Alexei Kaltchenkomentioning

confidence: 99%

See 1 more Smart Citation

Nearest-neighbor entropy estimators with weak metrics

Timofeev¹,

Kaltchenko²

2014

Advances in Mathematics of Communications

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A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak metrics, a new nearest-neighbor entropy estimator is constructed and has a parameter with which the estimator is optimized to reduce its bias. It is shown that estimator's variance is upper-bounded by a nearly optimal Cramér-Rao lower bound.2000 Mathematics Subject Classification. Primary: 58F15, 58F17; Secondary: 53C35.

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“…A generalisation of the nearest neighbour entropy estimator was introduced as a measure called Statentropy by Timofeev [50]. This estimator is defined as,…”

Section: Discrete-valued Discrete-time Entropy Rate Estimationmentioning

confidence: 99%

A Review of Shannon and Differential Entropy Rate Estimation

Feutrill

Roughan

2021

Entropy

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In this paper, we present a review of Shannon and differential entropy rate estimation techniques. Entropy rate, which measures the average information gain from a stochastic process, is a measure of uncertainty and complexity of a stochastic process. We discuss the estimation of entropy rate from empirical data, and review both parametric and non-parametric techniques. We look at many different assumptions on properties of the processes for parametric processes, in particular focussing on Markov and Gaussian assumptions. Non-parametric estimation relies on limit theorems which involve the entropy rate from observations, and to discuss these, we introduce some theory and the practical implementations of estimators of this type.

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Statistical estimation of measure invariants

Cited by 14 publications

References 34 publications

Methods of new technological developments of electric motors based on soft magnetic materials

Methods of new technological developments of electric motors based on soft magnetic materials

Nearest-neighbor entropy estimators with weak metrics

A Review of Shannon and Differential Entropy Rate Estimation

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