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Some Remarks on BLUP under the general linear model with linear Equality Restrictions

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Journal of Mathematical Research with Applications 2018年第5期38卷 496-508页

作者： Xingwei REN Leyi LIN Department of Mathematics Anhui Science and Technology University Wentian College Hohai University

In this paper, we give the representation of the best linear unbiased predictor(BLUP)of the new observations under Mrf. Through the representation, we give necessary and sufficient conditions that the estimators, OLSEs(ordinary least squares estimators) and BLUEs(best linear unbiased estimators), under Mfand Mrf, and the predictor, BLUP, under Mfcontinue to be the BLUP under Mrf, respectively.

关键词： general linear model restricted linear model BLUP OLSE BLUE

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance for the general linear model

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Journal of Mathematical Research and Exposition 2004年第2期24卷 280-284页

作者：李树有张宝学辽宁工学院数理系辽宁锦州121001 北京理工大学数学系

In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovest... 详细信息

关键词： general linear model generalized inverse orthogonal projector minimum norm quadratic unbiased estimator

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the general linear model

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Journal of Beijing Institute of Technology 2002年第1期11卷 97-100页

作者：张宝学罗季李馨北京理工大学应用数学系北京100081 东北师范大学数学系长春130024

Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.

关键词： general linear model orthogonal projector minimum norm quadratic unbiased estimator

A New general linear Convolution model for fMRI Data Process

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Journal of Electronic Science and Technology of China 2005年第1期3卷 68-71页

作者：袁宏陈华富尧德中 School of Life Science and Technology UESTC Chengdu 610054 China School of Life Science and Technology UESTC Chengdu 610054 China School of Applied Mathematics UESTC Chengdu 610054 China

general linear model (GLM) is the most popular method for functional magnetic resource imaging (fMRI) data analysis . However, its theory is imperfect. The key of this model is how to constitute the design-matrix to model the interesting effects better and separate noises better. For the purpose of detecting brain function activation , according to the principle of GLM,a new convolution model is presented by a new dynamic function convolving with design-matrix,which combining with t-test can be used to detect brain active signal. The fMRI imaging result of visual stimulus experiment indicates that brain activities mainly concentrate among v1and v2 areas of visual cortex, and also verified the validity of this technique.

关键词： fMRI general linear model t-test hemodynamic response function

model CHECKING FOR general linear ERROR-IN-COVARIABLES model WITH VALIDATION DATA

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Journal of Systems Science & Complexity 2010年第6期23卷 1153-1166页

作者： Pengjie DAI Zhihua SUN Peng WANG Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Business Renmin University of China Beijing 100872 China. School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Beijing 100049 China. Department of Mathematics Beijing Forestry University Beijing 100083 China.

In this paper, model checking problem is considered for general linear model when covariables are measured with error and an independent validation data set is available, Without assuming any error model structure between the true variable and the surrogate variable, the author first apply nonparametric method to model the relationship between the true variable and the surrogate variable with the help of the validation sample. Then the author construct a score-type test statistic through model adjustment. The large sample behaviors of the score-type test statistic are investigated. It is shown that the test is consistent and can detect the alternative hypothesis close to the null hypothesis at the rate n^-r with 0 ≤ r ≤1/2. Simulation results indicate that the proposed method works well. Key words general linear model, measurement error, model checking, validation data.

关键词： general linear model measurement error model checking validation data.

linear SUFFICIENCY IN THE general GAUSS-MARKOV model

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Applied Mathematics(A Journal of Chinese Universities) 2002年第1期17卷 85-92页

作者： Liu JinshanDept. of Math., Wuyi Univ.,Guangdong 529020. Dept. of Math. Wuyi Univ. Guangdong

This paper provides further contributions to the theory of linear sufficiency in the general Gauss-Markov model E(y)=Xβ,Var (y)=*** notion of linear sufficiency introduced by Baksalary and Kala(1981) and Drygas(1983) is extended for any specific estimable function c′β.Some general results with respect to the extended concept are *** essential result concerning the former notion is a direct consequence of this paper.

关键词： general linear model sufficiency BLUE linear sufficient statistics.

Efficiency of local minima and GLM techniques in sinkhole extraction from a LiDAR-based terrain model

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International Journal of Digital Earth 2019年第9期12卷 1067-1082页

作者： Péter Enyedi Melinda Pap Zoltán Kovács László Takács-Szilágyi Szilárd Szabó a Department of Physical Geography and Geoinformatics University of DebrecenDebrecenHungary Internet of Things Research Institute Eszterházy Károly University of Applied SciencesEgerHungary

The aim of this paper was to study reliable automated delineationpossibilities of karst sinkholes using a LiDAR-based digital terrain model(DTM) with pixel-based classifications. We applied two approaches toextract sinkholes: (1) general linear modeling (GLM) with morphometricindices derived from DTM;(2) and a local minima-based delineationusing only LiDAR DTM as the input layer. The outcome of the localminima was significantly different from the reference ones but found allthe sinkholes without previous knowledge of the area. The GLM-basedoutcome did not differ statistically from the reference. Results showedthat these approaches were efficient in detecting sinkholes based onLIDAR derivatives, and can be used for risk assessment and hazardpreparedness in karst areas: GLM had an overall accuracy of 89.5% andlocal minima had an accuracy of 92.3%;both methods identifiedsinkholes but also had commission errors, identifying depressions assinkholes.

关键词： Karst mapping sinkhole identification general linear model statistical evaluation sink fill

Geospatial Mapping of Soil Nitrate-Nitrogen Distribution Under a Mixed-Land Use System

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Pedosphere 2009年第4期19卷 434-445页

作者： S. LAMSAL C. M. BLISS D. A. GRAETZ School of Forest Resources and Conservation University of Florida USDA Forest Service Southern Research Station Soil and Water Science Department University of Florida

Mapping the spatial distribution of soil nitrate-nitrogen （NO3=N） is important to guide nitrogen application as well as to assess environmental risk of NO3-N leaching into the groundwater. We employed univariate and hybrid geostatistical methods to map the spatial distribution of soil NO3-N across a landscape in northeast Florida. Soil samples were collected from four depth increments （0-30, 30-60, 60-120 and 120-180 cm） from 147 sampling locations identified using a stratified random and nested sampling design based on soil, land use and elevation strata. Soil NO3-N distributions in the top two layers were spatially autocorrelated and mapped using lognormal kriging. Environmental correlation models for NO3-N prediction were derived using linear and non-linear regression methods, and employed to develop NO3-N trend maps. Land use and its related variables derived from satellite imagery were identified as important variables to predict NO3-N using environmental correlation models. While lognormal kriging produced smoothly varying maps, trend maps derived from environmental correlation models generated spatially heterogeneous maps. Trend maps were combined with ordinary kriging predictions of trend model residuals to develop regression kriging prediction maps, which gave the best NO3-N predictions. As land use and remotely sensed data are readily available and have much finer spatial resolution compared to field sampled soils, our findings suggested the efficacy of environmental correlation models based on land use and remotely sensed data for landscape scale mapping of soil NO3-N. The methodologies implemented are transferable for mapping of soil NO3-N in other landscapes.

关键词： environmental correlation general linear model kriging land use regression

Stability of fMRI activation:evidence from fusiform face area

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Stability of fMRI activation:evidence from fusiform face are...