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
We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑(i=1)^n xi(yi-h(x'iβ))=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, i...We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑(i=1)^n xi(yi-h(x'iβ))=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.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 propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear met...In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.展开更多
We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alte...We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.展开更多
This paper considers the problem of delay-dependent robust optimal H<sub>∞</sub> control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). Th...This paper considers the problem of delay-dependent robust optimal H<sub>∞</sub> control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H<sub>∞</sub> controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H<sub>∞</sub> noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H<sub>∞</sub> controller which minimizes the H<sub>∞</sub> noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.展开更多
This paper investigates the problem of robust optimal H<sub>∞</sub> control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncerta...This paper investigates the problem of robust optimal H<sub>∞</sub> control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H<sub><sub></sub></sub><sub>∞</sub> state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H<sub><sub><sub></sub></sub></sub><sub>∞</sub> noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.展开更多
Traditional methods for water table prediction have such defects as extensive calculation and reliance on the presupposition of a homogeneous and regular aquifer.Based on the fundamentals of the general regression neu...Traditional methods for water table prediction have such defects as extensive calculation and reliance on the presupposition of a homogeneous and regular aquifer.Based on the fundamentals of the general regression neural network(GRNN),this article sets up a GRNN model for water level prediction.Case study indicates that this model,even with limited information,has satisfactory prediction accuracy,which,coupled with a simple model structure and relatively high calculation efficiency,mean a vast application prospect for the model.展开更多
In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X)...In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X'β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞.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
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (ρ-mix...We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (ρ-mixing) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical process of the log-likelihood function and the true log-likelihood. The strong consistency of some penalized likelihood-based model selection criteria can be shown as an application of the LIL. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with the model dimension, and the penalty term has an order higher than O(log log n) but lower than O(n). Simulation studies are implemented to verify the selection consistency of Bayesian information criterion.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
基于Tweedie分布的广义线性模型(generalized linear model,简称GLM),并结合Kriging模型,发展了日降水量统计降尺度的GLM-Kriging模型.首先用GLM拟合研究区域内日降水量与数值模式输出的影响局地降水的物理量之间的关系,日降水量的空间...基于Tweedie分布的广义线性模型(generalized linear model,简称GLM),并结合Kriging模型,发展了日降水量统计降尺度的GLM-Kriging模型.首先用GLM拟合研究区域内日降水量与数值模式输出的影响局地降水的物理量之间的关系,日降水量的空间相关性反映在模型的残差中;然后用Kriging模型来拟合GLM的随机化百分位残差(randomized quantile residuals,简称RQ残差).结合NCEP再分析资料应用于2007年7月沂沭泗流域的42站日降水观测,结果表明GLM-Kriging降尺度模型较好地还原了主要降水过程,整体上取得了较高的准确度,可用于气候变化影响评估或数值天气预报产品的释用,还可进一步扩展为日降水量的时空统计模型.展开更多
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.
文摘We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑(i=1)^n xi(yi-h(x'iβ))=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.
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.
文摘In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.
文摘We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.
文摘This paper considers the problem of delay-dependent robust optimal H<sub>∞</sub> control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H<sub>∞</sub> controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H<sub>∞</sub> noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H<sub>∞</sub> controller which minimizes the H<sub>∞</sub> noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.
文摘This paper investigates the problem of robust optimal H<sub>∞</sub> control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H<sub><sub></sub></sub><sub>∞</sub> state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H<sub><sub><sub></sub></sub></sub><sub>∞</sub> noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.
文摘Traditional methods for water table prediction have such defects as extensive calculation and reliance on the presupposition of a homogeneous and regular aquifer.Based on the fundamentals of the general regression neural network(GRNN),this article sets up a GRNN model for water level prediction.Case study indicates that this model,even with limited information,has satisfactory prediction accuracy,which,coupled with a simple model structure and relatively high calculation efficiency,mean a vast application prospect for the model.
基金supported by the President Foundation (Grant No. Y1050)the Scientific Research Foundation(Grant No. KYQD200502) of GUCAS
文摘In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X'β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞.
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.
文摘We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (ρ-mixing) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical process of the log-likelihood function and the true log-likelihood. The strong consistency of some penalized likelihood-based model selection criteria can be shown as an application of the LIL. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with the model dimension, and the penalty term has an order higher than O(log log n) but lower than O(n). Simulation studies are implemented to verify the selection consistency of Bayesian information criterion.
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.
文摘基于Tweedie分布的广义线性模型(generalized linear model,简称GLM),并结合Kriging模型,发展了日降水量统计降尺度的GLM-Kriging模型.首先用GLM拟合研究区域内日降水量与数值模式输出的影响局地降水的物理量之间的关系,日降水量的空间相关性反映在模型的残差中;然后用Kriging模型来拟合GLM的随机化百分位残差(randomized quantile residuals,简称RQ残差).结合NCEP再分析资料应用于2007年7月沂沭泗流域的42站日降水观测,结果表明GLM-Kriging降尺度模型较好地还原了主要降水过程,整体上取得了较高的准确度,可用于气候变化影响评估或数值天气预报产品的释用,还可进一步扩展为日降水量的时空统计模型.