Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the General Linear Model

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.

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.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance for the General Linear Model

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。

西北印度洋鸢乌贼(Sthenoteuthis oualaniensis)灯光罩网渔业CPUE标准化研究

单位捕捞努力量渔获量(CPUE)是渔业资源评估的前提和基础,为了更好地评估西北印度洋鸢乌贼(Sthenoteuthis oualaniensis)资源丰度,掌握鸢乌贼资源分布与时空因子及海洋环境因子之间的关系,利用广义线性模型(GLM)和用广义加性模型(GAM),结合时空因子及海洋环境因子对2015~2021年西北印度洋鸢乌贼灯光罩网渔业CPUE进行标准化研究,并评价各因子对CPUE的影响。GLM模型结果显示,6个变量对CPUE影响显著,依次为年份(Year)、月份(Month)、经度(lon)、纬度(lat)、海表面温度(SST)、叶绿素a浓度(chl a);依次加入六个显著变量构建GAM模型,并通过对不同GAM模型的AIC值进行比较,结果显示包含6个变量的GAM模型AIC值最小且模型最优,对CPUE偏差的解释率为37.80%。研究表明,西北印度洋鸢乌贼高CPUE主要出现在9月至翌年3月期间,13°N~20°N、58°E~66°E、SST为26.0~29.0°C、chl a为0.07~0.73 mg/m^(3)的海域内。整体而言,基于GLM模型和GAM模型对西北印度洋鸢乌贼灯光罩网渔业CPUE标准化研究,能够较好地反映鸢乌贼资源的丰度变化情况。

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 $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . 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 S n ?1 → 0, as the sample size n → ∞.

MODEL CHECKING FOR GENERAL LINEAR ERROR-IN-COVARIABLES MODEL WITH VALIDATION DATA

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.

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.