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...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.展开更多
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...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-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.展开更多
Abstract Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the disper...Abstract Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.展开更多
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 m...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.展开更多
This paper provides further contributions to the theory of linear sufficiency in the general Gauss-Markov model E(y)=Xβ,Var (y)=V.The notion of linear sufficiency introduced by Baksalary and Kala(1981) and Drygas(198...This paper provides further contributions to the theory of linear sufficiency in the general Gauss-Markov model E(y)=Xβ,Var (y)=V.The 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 obtained.An essential result concerning the former notion is a direct consequence of this paper.展开更多
In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least s...In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem： a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-r, 0 ≤ r 〈 1/2. Simulation results show that both tests perform satisfactorily.展开更多
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 bet...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.展开更多
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...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.展开更多
A major natural hazard associated with LGOM （Legnica-Glogow Copper Mining） mining is the dynamic phenomena occurrence, physically observed as seismic tremors. Some of them generate effects in the form of relaxations...A major natural hazard associated with LGOM （Legnica-Glogow Copper Mining） mining is the dynamic phenomena occurrence, physically observed as seismic tremors. Some of them generate effects in the form of relaxations or bumps. Long-term observations of the rock mass behaviour indicate that the degree of seismic hazard, and therefore also seismic activity in the LGOM area, is affected by the great depth of the copper deposit, high-strength rocks as well as the ability of rock mass to accumulate elastic energy. In this aspect, the effect of the characteristics of initial stress tensor and the orientation of considered mining panel in regards to its components must be emphasised. The primary objective of this study is to answer the question, which of the factors considered as ＂influencing＂ the dynamic phenomena occurrence in copper mines have a statistically significant effect on seismic activity and to what extent. Using the general linear model procedure, an attempt has been made to quantify the impact of different parameters, including the depth of deposit, the presence of goaf in the vicinity of operating mining panels and the direction of mining face advance, on seismic activity based on historical data from 2000 to 2010 concerned with the dynamic phenomena recorded in different mining panels in Rudna mine. The direction of mining face advance as well as the goaf situation in the vicinity of the mining panel are of the greatest interest in the case of the seismic activity in LGOM. It can be assumed that the appropriate manipulation of parameters of mining systems should ensure the safest variant of mining method under specific geological and mining conditions.展开更多
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 si...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.展开更多
An investigation using recall questionnaires was conducted in winter and autumn 2006 to evaluate the time-activity patterns in Chongqing,China.The average time spent in seven microenvironments(MEs)including outdoors,t...An investigation using recall questionnaires was conducted in winter and autumn 2006 to evaluate the time-activity patterns in Chongqing,China.The average time spent in seven microenvironments(MEs)including outdoors,transit,living room,bedroom,kitchen,classroom/office,and other indoors were found to be about 3.5,1.1,2.5,9.7,1.4,4.2,and 1.7 h per day,respectively.According to the results of a nonparametric test,the sampling period and day of week were significant for the variation of the time spent in all MEs except for transit and outdoors.The time budget was analyzed using a general linear model(GLM),which exhibited significant variability by demographic factors such as gender,age,residence,education,and household income.展开更多
文摘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.
基金Supported by China Mathematics Tian Yuan Youth Foundation (10226024) and China Postdoctoral Science Foundation.
文摘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-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.
基金Partially supported by the National Natural Science Foundation of China (No.10271010)the Natural Science Foundation of Beijing and a Project of Science and Technology of Beijing Education Committee.
文摘Abstract Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.
基金Supported by National Natural Science Foundation of China (No.90208003, 30200059), the 973 Project (No. 2003CB716106), Doctor training Fund of MOE, P.R.C., and Fok Ying Tong Education Foundation (No.91041)
文摘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.
基金the Natural Science Foundation of Guangdong Province(0 1 0 4 86 )
文摘This paper provides further contributions to the theory of linear sufficiency in the general Gauss-Markov model E(y)=Xβ,Var (y)=V.The 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 obtained.An essential result concerning the former notion is a direct consequence of this paper.
基金supported by the National Natural Science Foundation of China (No. 10901162,10926073)China Postdoctoral Science Foundation and the President Fund of GUCAS+1 种基金the foundation of the Key Laboratory of Random Complex Structures and Data Science, CASsupported by a research grant from the Research Committee, The Hong Kong Polytechnic University
文摘In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem： a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-r, 0 ≤ r 〈 1/2. Simulation results show that both tests perform satisfactorily.
基金This research is supported by the National Natural Science Foundation of China （10901162, 10926073）, the President Fund of GUCAS and China Postdoctoral Science Foundation.
文摘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.
基金Project supported by the United States Department of Agriculture through the "Nutrient Science for Improved Watershed Management" program (No.2002-00501)
文摘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.
文摘A major natural hazard associated with LGOM （Legnica-Glogow Copper Mining） mining is the dynamic phenomena occurrence, physically observed as seismic tremors. Some of them generate effects in the form of relaxations or bumps. Long-term observations of the rock mass behaviour indicate that the degree of seismic hazard, and therefore also seismic activity in the LGOM area, is affected by the great depth of the copper deposit, high-strength rocks as well as the ability of rock mass to accumulate elastic energy. In this aspect, the effect of the characteristics of initial stress tensor and the orientation of considered mining panel in regards to its components must be emphasised. The primary objective of this study is to answer the question, which of the factors considered as ＂influencing＂ the dynamic phenomena occurrence in copper mines have a statistically significant effect on seismic activity and to what extent. Using the general linear model procedure, an attempt has been made to quantify the impact of different parameters, including the depth of deposit, the presence of goaf in the vicinity of operating mining panels and the direction of mining face advance, on seismic activity based on historical data from 2000 to 2010 concerned with the dynamic phenomena recorded in different mining panels in Rudna mine. The direction of mining face advance as well as the goaf situation in the vicinity of the mining panel are of the greatest interest in the case of the seismic activity in LGOM. It can be assumed that the appropriate manipulation of parameters of mining systems should ensure the safest variant of mining method under specific geological and mining conditions.
文摘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.
基金This work was supported by the Environmental Decision Making in China(DEMAND)funded by the Norwegian Agency for Development Cooperation(No.CHN-2087).
文摘An investigation using recall questionnaires was conducted in winter and autumn 2006 to evaluate the time-activity patterns in Chongqing,China.The average time spent in seven microenvironments(MEs)including outdoors,transit,living room,bedroom,kitchen,classroom/office,and other indoors were found to be about 3.5,1.1,2.5,9.7,1.4,4.2,and 1.7 h per day,respectively.According to the results of a nonparametric test,the sampling period and day of week were significant for the variation of the time spent in all MEs except for transit and outdoors.The time budget was analyzed using a general linear model(GLM),which exhibited significant variability by demographic factors such as gender,age,residence,education,and household income.
