A New General Linear Convolution Model for fMRI Data Process

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.

Asymptotic Normality of Multi-Dimension Quasi Maximum Likelihood Estimate in Generalized Linear Models withAdaptive Design

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.

LINEAR SUFFICIENCY IN THE GENERAL GAUSS-MARKOV MODEL

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.

Testing Linearity of Nonparametric Component in Partially Linear Model

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.

Testing Equality of Nonparametric Functions in Two Partially Linear Models

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.

Delay-Dependent Robust H∞ Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

This paper considers the problem of delay-dependent robust optimal H∞ 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∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ 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∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

Robust Optimal H∞ Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ 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∞ 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∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

GLM和GAM模型研究东黄海鲐资源渔场与环境因子的关系

鲐是我国近海重要中上层鱼类,研究其资源变动、渔场分布与时空、海洋环境因子之间的关系有利于该资源的合理开发和利用。根据1998-2004年我国东黄海大型鲐围网渔业的生产统计和时间、空间、表温、表层盐度、表温梯度、表温的月差异等环境数据,利用广义可加模型(GAM)和广义线性模型(GLM)对鲐资源丰度和环境因子的关系进行研究。结果表明,在南部海域,作业渔场集中在122.5°E^124°E、26.5°N^28°N,适宜表温26.5~30℃,适宜表层盐度33.3~34.3,并明显集中在锋区周边海域;在北部海域,作业渔场集中在122.5°E^125.5°E、33°N^37.5°N,适宜表温15~20℃,适宜表层盐度31.3~32.3,集中在冷水区边缘海域。相对资源密度指数大于0.5的海域为122°30′E^124°30′E、26°30′N^28°N,122°30′E^125°30′E、33°N^34°30′N和124°E^125°E、34°30′N^37°N。研究认为,南北不同海域鲐分布的适宜表温和表层盐度差异明显。影响鲐资源丰度的环境因子重要性依次为时间、空间和海洋环境。

基于GLM模糊评价在煤矿安全中的应用

煤矿安全评价是现代绿色矿山建设的主要指标之一。为对煤矿安全进行有效的评价,综合分析影响煤矿安全的人员因素、地质因素、技术设备因素、环境因素等各项指标。应用广义线性理论和SAS统计分析方法,建立基于GLM模糊评价模型。通过计算各项指标对应等级的煤矿安全影响权重珚ωij,结合模糊综合评价方法得出煤矿的安全生产状况,同时通过优势比分析各指标的敏感性因子,得出防范指标危险性的有效措施。研究表明:该模型依据标准整理数据,操作性强,较准确地得出煤矿安全的状况,为煤矿的安全评价和管理决策提供依据。

一类非连续数据的GLM模型的应用

分析了因变量取有限个不连续点值的一种情况，给出了因变量Ｙ取值城中任一点值 的概率估计．并运用这种方法，对ＲＫ手术的结果作出了预测．

基于二值型数据的荣成天鹅湖菲律宾蛤仔空间分布与环境因子关系研究

为了利用简化的二值型渔业数据研究物种空间分布与环境因子之间的关系。基于2017年四个季度山东半岛荣成天鹅湖的菲律宾蛤仔(Ruditapes philippinarum)实地调查数据,比较了广义加性模型(GAM)和广义线性模型(GLM)在处理二值型菲律宾蛤仔渔业数据的表现,并利用GAM模型研究了天鹅湖的菲律宾蛤仔空间分布与环境因子之间的关系。研究显示:GAM模型在偏差解释率、模型评估效果和预测性能方面均优于GLM模型;水深、总有机质含量和叶绿素a浓度显著影响菲律宾蛤仔的空间分布(P<0.05)。菲律宾蛤仔的出现概率随叶绿素a浓度增加逐渐上升,随总有机质含量和水深的增加逐渐下降。研究结果表明,二值型简化数据能够有效地揭示菲律宾蛤仔空间分布与环境因子的关系。

基于GLM的社会医疗保险住院费用分析

传统的回归模型经常被用来分析医疗保险费用.然而,传统回归模型在分析医疗保险费用时存在很大的缺陷.本文引进的广义线性模型解决了传统回归模型的缺陷,并将这个模型应用到对社会医疗保险住院费用的分析中.

Prediction of Water Table Based on General Regression Neural Network

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.

On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models

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 →∞.

Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models

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.

Law of iterated logarithm and model selection consistency for generalized linear models with independent and dependent responses

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.

Model Checking for a General Linear Model with Nonignorable Missing Covariates

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.

中国大陆阿根廷滑柔鱼鱿钓渔业CPUE标准化

阿根廷滑柔鱼是我国重要的头足类渔业之一,单位捕捞努力量渔获量(CPUE)标准化是对其资源进行评估的重要内容。研究根据2000—2010年中国大陆在西南大西洋的鱿钓产量统计数据和卫星遥感获得的海洋环境数据(表温,表温水平梯度,海面高度,叶绿素浓度),利用广义线性模型(general linear model,GLM)和广义加性模型(generalized additive model,GAM)对中国大陆西南大西洋阿根廷滑柔鱼渔业CPUE标准化。GLM模型结果表明,年、纬度、表温以及交互项年与纬度对CPUE影响最大。GAM模型研究结果则表明年、月、经度、纬度、表温、海面高度以及交互项年与纬度、年与经度对CPUE影响较大。根据AIC准则,包含上述8个显著变量的GAM模型为最佳模型,对CPUE的解释率为49.20%。高CPUE出现在夏季表温为12～16℃、海面高度为-20～20 cm和46.5°～48.5°S范围内。研究表明,GAM模型较GLM模型更适合用于西南大西洋阿根廷滑柔鱼渔业CPUE标准化。

基于Tweedie分布的日降水量统计降尺度模型

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.

应用一般线性模型估算鲐、鲹大型灯光围网渔业的捕捞效率

大型灯光围网是我国近海捕捞鲐、鲹的主要作业方式之一,探讨和估算捕捞效率对其渔业资源评估和管理有着重要的意义。根据1998-2003年东黄海我国鲐、鲹大型机轮灯光围网生产统计数据,利用一般线性模型对其捕捞效率进行了估算,讨论了线性模型误差结构的选择及数据变换对结果的影响。根据鲐、鲹单位捕捞努力量的渔获量(CPUE)数据呈正偏,以及CPUE均值与方差在对数尺度下的线性关系,选择了负二项分布、伽马分布与对数正态分布作为误差分布。研究表明,由于CPUE零值的存在,其对误差分布结构有很大影响。当采用最大似然估计时,对数正态分布与伽马分布的CPUE需加一常数(δ),δ取值对结果有较大影响,随δ增大将使估计的捕捞效率对比度得到压缩。为了避免δ取值的影响,同时采用了Delta-GLM方法。通过不同模型的比较,选择了Delta-负二项或Delta-伽马方法。根据Delta-负二项或Delta-伽马方法估算结果,各渔业公司间的捕捞效率存在很大的差异,且具有明显的区域性。32°N以北海区,捕捞效率高低依次为苏渔、辽渔、青渔、舟渔、宁渔、沪渔;台湾东北部海区,捕捞效率高低依次为苏渔、辽渔、舟渔、沪渔、宁渔、青渔。