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A New Phasor estimator for PMU Applications:P Class and M Class

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Journal of Modern Power Systems and Clean Energy 2020年第1期8卷 55-66页

作者： Jose R.Razo-Hernandez Arturo Mejia-Barron David Granados-Lieberman Martin Valtierra-Rodriguez Jose F.Gomez-Aguilar ENAP-Research Group Facultad de IngenieríaUniversidad Autónoma de Querétaro(UAQ)San CayetanoC.P.76807México ENAP-Research Group Departamento de Ingeniería ElectromecánicaInstituto Tecnológico Superior de Irapuato(ITESI)Colonia El CopalC.P.36821México CONACyT-Centro Nacional de Investigación y Desarrollo Tecnológico(CENIDET) Tecnológico Nacional de MéxicoInterior Internado Palmira S/NCol.PalmiraC.P.62490México

Phasor measurement units(PMUs)are fundamental tools in the applications of modern power systems,where synchronized phasor estimations are needed.The accuracy and dynamic performance requirements for phasor,frequency,and rate of change of frequency(ROCOF)estimations are established in the IEEE Std.C37.118.1-2011 along with the IEEE Std.C37.118.1 a-2014,where two PMU performances are suggested:P class filters for applications requiring fast response and M class filters for applications requiring high rejection to aliased signals.In this paper,a methodology to design new phasor estimators that satisfy the P class and M class requirements in PMUs is presented.The proposed methodology is based on finite impulse response filters,brick-wall filters,and complex filter design concepts,where frequency range,time performance,harmonic rejection and out-of-band interference requirements are considered in its design.A comparative analysis using the reference model given by the IEEE Std.C37.118.1 is presented.The results show the effectiveness of the phasor estimators under steady-state and dynamic conditions according to the PMU standard,making them suitable tools for applications in power systems.

关键词： Brick-wall filter complex filter IEEE Std.C37.118.1 M class P class phasor measurement unit(PMU) phasor estimator

Edgeworth expansion of the Studentized product-limit estimator for truncated and censored data

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Science China Mathematics 2000年第5期43卷 495-508页

作者：孙六全 Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expan-sion is close to the exact distribu... 详细信息

关键词： truncated and censored data Studentized product-limit estimator asymptotic normality Edge- worth expansion.

On Consistency of the Nearest Neighbor estimator of the Density Function and Its Applications

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Acta Mathematica Sinica,English Series 2019年第5期35卷 703-720页

作者： Yi WU Xue Jun WANG School of Mathematical Sciences Anhui University

In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.

关键词： Nearest neighbor estimator weak consistency strong consistency uniform consistency hazard rate function estimator

Edgeworth expansion for the bivariate product-limit estimator

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Science China Mathematics 1997年第11期40卷 1136-1147页

作者：王启华 Institute of Applied Mathematics Chinese Academy of ScienceBeijing 100080China

Let S(s,t) be the bivariate survival function.Let Sn(s,t) be the bivariate product limit estimator proposed by Campbell and Foldes.The one-term Edgeworth expansion for Sn(s,t) is established by expressing logSn(s,t)-l... 详细信息

关键词： random censorship bivariate product limit estimator Edgeworth expansion.

LEAST SQUARES estimator FOR PATH-DEPENDENT MCKEAN-VLASOV SDES VIA DISCRETE-TIME OBSERVATIONS

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Acta Mathematica Scientia 2019年第3期39卷 691-716页

作者：任盼盼吴奖伦 Department of Mathematics Computational Foundry Swansea University Bay Campus

In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.

关键词： McKean-Vlasov stochastic differential equation tamed Euler-Maruyama scheme weak monotonicity least squares estimator consistency asymptotic distribution

A LAW OF THE ITERATED LOGARITHM FOR NEIGHBOR-TYPE REGRESSION FUNCTION estimator

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Chinese Annals of Mathematics,Series B 1992年第2期13卷 180-195页

作者：洪圣岩 Department of Mathematics Anhui University Hefei Anhui 230039 China

Let (X, Y) be a two-dimensional random variable. A law of the iterated logarithm is established for a smoothed neighbor-typo estimator of the regression function m(x)=E(Y|X=x) under conditions much weaker than needed for the Nadaraya-Watson estimator. Also the sharp pointwise rates of strong consistency of this estimator is discussed in detail.

关键词： estimator neighbor smoothed consistency kernel sharp logarithm iterated Watson bandwidth

THE CHUNG-SMIRNOV LAW FOR THE PRODUCT-LIMIT estimator UNDER RANDOM CENSORSHIP

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Chinese Annals of Mathematics,Series B 1991年第1期12卷 96-105页

作者：顾鸣高 McGill University MontrealCanada.

The maximal deviation of the product limit estimator on the whole line isinvestigated.The analogue of Chung-Smirnov law of iterated logarithm is proved undervery mild conditions on censoring.An improved oonvergenoe rate is found and shown tobe best possible The result is proved by an i.***.d.representation scheme of the productlimit estimator on the whole line.Improved rates of convergence for the i.***.d.representation on compact set are also derived.

关键词： estimator deviation analogue maximal logarithm iterated proof biome apply Singh

Necessary and sufficient conditions for the existence of the UMRE estimator in growth curve models

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Science China Mathematics 1995年第3期38卷 287-297页

作者：吴启光 Institute of Systems Science Chinese Academy of Sciences Beijing 100080 China

The necessary and sufficient conditions are derived for the existence of the uniformly minimum risk equivariant (UMRE) estimator of regression coefficient matrix in normal growth carve models with arbitrary covariance matrix or uniform oovananoe structure or serial covariance structure under an affine group and a transitive group of transformations for quadratic losses and matrix losses, respectively.

关键词： uniformly miniusum risk equivariant estimator affine group of transformations traesitive group of transformations quadratic loss matrix loss.

Admissibilities of linear estimator in a class of linear models with a multivariate t error variable

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Science China Mathematics 2010年第8期53卷 2011-2019页

作者： YANG GuoQing 1 & WU QiGuang 2 1 Department of Mathematics,Tongji University,Shanghai 200092,China 2 Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China Department of Mathematics Tongji University Shanghai China Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

This paper discusses admissibilities of estimators in a class of linear models,which include the following common models:the univariate and multivariate linear models,the growth curve model,the extended growth curve model,the seemingly unrelated regression equations,the variance components model,and so on.It is proved that admissible estimators of functions of the regression coefficient β in the class of linear models with multivariate t error terms,called as Model II,are also ones in the case that error terms have multivariate normal distribution under a strictly convex loss function or a matrix loss function.It is also proved under Model II that the usual estimators of β are admissible for p 2 with a quadratic loss function,and are admissible for any p with a matrix loss function,where p is the dimension of β.

关键词： multivariate t distribution convex loss quadratic loss matrix loss admissible estimator