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ON STABLE PERTURBATIONS OF THE STIFFLY weighted PSEUDOINVERSE AND weighted least squares PROBLEM

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Journal of Computational Mathematics 2005年第5期23卷 527-536页

作者： Wei E CHINA NORMAL UNIV

In this paper we study perturbations of the stiffly weighted pseudoinverse （W^1/2 A）^＋W^1/2 and the related stiffly weighted least squares problem, where both the matrices A and W are given with W positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices A = A ＋ δA satisfy several row rank preserving conditions.

关键词： Stiffly weighted pseudoinverse weighted least squares Perturbation Stability

Consistency and Asymptotic Property of a weighted least squares Method for Networked Control Systems

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Chinese Journal of Chemical Engineering 2014年第7期22卷 754-761页

作者：张聪叶昊 Tsinghua National Laboratory for Information Science and Technology Department of Automation Tsinghua University

In this paper, we study the problems related to parameter estimation of a single-input and single-output networked control system, which contains possible network-induced delays and packet dropout in both of sensor-to-controller path and controller-to-actuator path. A weighted least squares(WLS) method is designed to estimate the parameters of plant, which could overcome the data uncertainty problem caused by delays and dropout. This WLS method is proved to be consistent and has a good asymptotic property. Simulation examples are given to validate the results.

关键词： Networked control system Network-induced delay Packet dropout weighted least squares Consistency Asymptotic property

Multi-period Power System State Estimation with PMUs Under GPS Spoofing Attacks

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Journal of Modern Power Systems and Clean Energy 2020年第4期8卷 597-606页

作者： Paresh Risbud Nikolaos Gatsis Ahmad Taha Department of Electrical and Computer Engineering University of Texas at San AntonioSan AntonioUSA IEEE

This paper introduces a dynamic network model together with a phasor measurement unit(PMU)measurement model suitable for power system state estimation under spoofing attacks on the global positioning system(GPS)receivers of *** spoofing attacks may introduce time-varying phase offsets in the affected PMU *** algorithm is developed to jointly estimate the state of the network,which amounts to the nodal voltages in rectangular coordinates,as well as the time-varying *** algorithm features closedform *** effectiveness of the algorithm is verified on the standard IEEE transmission *** is numerically shown that the estimation performance is improved when the dynamic network model is accounted for compared with a previously reported static approach.

关键词： Dynamic state equation global positioning system(GPS)spoofing phasor measurement unit(PMU) state estimation time synchronization weighted least squares

Influence of climatic conditions,topography and soil attributes on the spatial distribution of site productivity index of the species rich forests of Jalisco,Mexico

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Journal of Forestry Research 2014年第1期25卷 87-95页

作者： Adel Mohamed Robin M.Reich Raj Khosla C.Aguirre-Bravo Martin Mendoza Briseo Department of Ecology and Rangeland Stewardship Desert Research Center Department of Forest and Rangeland Stewardship Colorado State University Department of Soil and Crop Sciences Colorado State University USDA Forest Service Colegio de Postgraduados

This paper presents an approach based on field data to model the spatial distribution of the site productivity index （SPI） of the diverse forest types in Jalisco, Mexico and the response in SPI to site and cli-matic conditions. A linear regression model was constructed to test the hypothesis that site and climate variables can be used to predict the SPI of the major forest types in Jalisco. SPI varied significantly with topog-raphy （elevation, aspect and slope）, soil attributes （pH, sand and silt）, climate （temperature and precipitation zones） and forest type. The most important variable in the model was forest type, which accounted for 35% of the variability in SPI. Temperature and precipitation accounted for 8 to 9% of the variability in SPI while the soil attributes accounted for less than 4% of the variability observed in SPI. No significant differences were detected between the observed and predicted SPI for the individual forest types. The linear regression model was used to develop maps of the spatial variability in predicted SPI for the individual forest types in the state. The spatial site productivity models developed in this study provides a basis for understanding the complex relationship that exists between forest productivity and site and climatic conditions in the state. Findings of this study will assist resource managers in making cost-effective decisions about the management of individual forest types in the state of Jalisco, Mexico.

关键词： Best management practices climate change spatial predic-tions tropical dry forests weighted least squares

Research on the discrimination methods of algae based on the fluorescence excitation spectra

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Acta Oceanologica Sinica 2010年第4期29卷 116-128页

作者： HU Xupeng SU Rongguo ZOU Weiming REN Shijun WANG Hongtao CHAI Xiaoping WANG Yiming Zhejiang Provincial Zhoushan Marine Ecological Environmental Monitoring Station Zhoushan 316000 China College of Chemistry and Chemical Engineering Ocean University of China Qingdao 266100 China

The excitation spectra of chlorophyll （Chl） fluorescence can be used to differentiate phytoplankton populations at phylum level in vivo and in situ within a few *** investigated phytoplankton divisions （Dinophyta,Bacillariophyta,Chrysophyta,Cyanophyta,Cryptophyta,Chlorophyta） are each characterized by a specific composition of photosynthetic antenna pigments and,consequently,by a specific excitation spectrum of the Chl *** excitation spectra （emission of 680 nm and excitation of 400–600 nm） of every division were obtained from several species per division by a F4500 fluorescence ***’s linear discriminant analysis of the norm spectra shows that the divisions could be *** discrimination method,established by multivariate linear regression and weighted least squares,was used to differentiate the phytoplankton samples cultured in the laboratory and samples collected from the Jiaozhao Bay at division *** correctly discriminated samples were more than 94% for single algal species ones,more than 84% for simulatively mixed ones,more than 83% for real mixed ones and 100% for samples collected from the Jiaozhou Bay for the dominant *** method for phytoplankton differentiation described here can be applied to routine checking by fluorescence spectrophotometer,and benefit the monitoring and supervision tasks related to phytoplankton populations in the marine environments.

关键词： fluorescence spectrum discrimination weighted least squares phytoplankton

A Sequential Regression Model for Big Data with Attributive Explanatory Variables

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Journal of the Operations Research Society of China 2015年第4期3卷 475-488页

作者： Qing-Ting Zhang Yuan Liu Wen Zhou Zhou-Wang Yang University of Science and Technology of China Hefei 230026China

As the applications for modeling of big data and analysis advance in scope,computational efficiency faces greater challenges in terms of storage and *** many practical problems,a great amount of historical data is sequentially collected and used for online statistical *** modeling sequential data,we propose a sequential linear regression method that extracts essential information from historical *** carefully selected information is then utilized to update a model according to a sequential estimation *** this technique,the earlier data no longer needs to be stored,and the sequential updating is computationally efficient in speed and storage.A weighted strategy is introduced on the current model to determine the impact of data from different *** compared with estimation methods that use historical data,our numerical experiments demonstrate that our solution increases the speed while decreasing the storage load.

关键词： Big data Attributive explanatory variables Periodic spline weighted least squares Sequential estimation

RELATIONSHIP BETWEEN THE STIFFLY weightedPSEUDOINVERSE AND MULTI-LEVEL CONSTRAINED PSEUDOINVERSE

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Journal of Computational Mathematics 2004年第3期22卷 427-436页

作者： Mu-shengWei DepartmentofMathematics EastChinaNormalUniversityShanghai200062China

It is known that for a given matrix A of rank r, and a set D of positive diagonal matrices, supw∈D‖（W^1/2A)+W^1/2‖ = (miniσ+(A^(i))^-1, in which (A^(i) is a submatrix of A formed with r = (rank(A)) rows of A, such that (A^(i) has full row rank r. In many practical applications this value is too large to be used. In this paper we consider the case that both A and W(∈D) are fixed with W severely stiff. We show that in this case the weighted pseudoinverse (W^1/2‖A)+W^1/2‖ is close to a multilevel constrained weighted pseudoinverse therefore ‖(W^1/2A)+W^1/‖2 is uniformly *** also prove that in this case the solution set the stiffly weighted least squares problem is close to that of corresponding multi-level constrained least squares problem.

关键词： Multi-Level constrained pseudoinverse Stiff weighted least squares

Multilevel Modelling for Surgical Tool Calibration Using LINEX Loss Function

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Computers, Materials & Continua 2022年第10期73卷 1691-1706页

作者： Mansour F.Yassen Department of Mathematics College of Science and Humanities in Al-AflajPrince Sattam Bin Abdulaziz UniversityAl-Aflaj11912Saudi Arabia Department of Mathematics Faculty of ScienceDamietta UniversityNew Damietta34517DamiettaEgypt

Quantifying the tool–tissue interaction forces in surgery can be utilized in the training of inexperienced surgeons,assist them better use surgical tools and avoid applying excessive *** voltages read from strain gauges are used to approximate the unknown values of implemented *** this objective,the force-voltage connection must be quantified in order to evaluate the interaction forces during *** progress of appropriate statistical learning approaches to describe the link between the genuine force applied on the tissue and numerous outputs obtained from sensors installed on surgical equipment is a key *** this study,different probabilistic approaches are used to evaluate the realized force on tissue using voltages read from strain gauges,including bootstrapping,Bayesian regression,weighted least squares regression,and multi-level *** from the proposed models are more precise than the maximum likelihood and restricted maximum likelihood *** suggested methodologies are proficient of assessing tool-tissue interface forces with an adequate level of accuracy.

关键词： Surgical tool weighted least squares multi-level modelling Bayesian approach

weighted estimation of single index models with right censored responses

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Science China Mathematics 2011年第3期54卷 479-514页

作者： WANG YanHua1, LI XiaYan2, WANG QiHua3 & HE ShuYuan4 1School of Sciences, Beijing Institute of Technology, Beijing 100081, China 2Department of Mathematics, University of Science and Technology of China, Hefei 230026, China 3Chinese Academy of Mathematics and System Science, Beijing 100080, China 4School of Mathematical Sciences, Capital Normal University, Beijing 100048, China School of Sciences Beijing Institute of Technology Beijing China Department of Mathematics University of Science and Technology of China Hefei China Chinese Academy of Mathematics and System Science Beijing China School of Mathematical Sciences Capital Normal University Beijing China

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

关键词： single index models random censorship central limit theorem law of the iterated logarithm weighted least squares unknown link function