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Confidence Intervals of Variance Functions in generalized linear model

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Acta Mathematicae Applicatae Sinica 2006年第3期22卷 353-368页

作者： Yong Zhou Dao-ji Li Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.

关键词： Nonlinear time series model variance function conditional heteroscedastie variance generalized linear model local polynomial fitting α-mixing

Assessing the Effect of Climate Factors on Dengue Incidence via a generalized linear model

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Open Journal of Applied Sciences 2021年第4期10卷 549-563页

作者： Ayuna Sulekan Jamaludin Suhaila Nurmarni Athirah Abdul Wahid Department of Mathematical Sciences Faculty of Science Universiti Teknologi Malaysia Johor Bahru Malaysia UTM Centre for Industrial and Applied Mathematics (UTM-CIAM) Ibnu Sina Institute for Scientific and Industrial Research Universiti Teknologi Malaysia Johor Bahru Malaysia

Changes in climate factors such as temperature, rainfall, humidity, and wind speed are natural processes that could significantly impact the incidence of infectious diseases. Dengue is a widespread disease that has often been documented when it comes to the impact of climate change. It has become a significant concern, especially for the Malaysian health authorities, due to its rapid spread and serious effects, leading to loss of life. Several statistical models were performed to identify climatic factors associated with infectious diseases. However, because of the complex and nonlinear interactions between climate variables and disease components, modelling their relationships have become the main challenge in climate-health studies. Hence, this study proposed a generalized linear model (GLM) via Poisson and Negative Binomial to examine the effects of the climate factors on dengue incidence by considering the collinearity between variables. This study focuses on the dengue hot spots in Malaysia for the year 2014. Since there exists collinearity between climate factors, the analysis was done separately using three different models. The study revealed that rainfall, temperature, humidity, and wind speed were statistically significant with dengue incidence, and most of them shown a negative effect. Of all variables, wind speed has the most significant impact on dengue incidence. Having this kind of relationships, policymakers should formulate better plans such that precautionary steps can be taken to reduce the spread of dengue diseases.

关键词： Climate Factors Dengue generalized linear model Poisson Negative Binomial

Investigating Performances of Some Statistical Tests for Heteroscedasticity Assumption in generalized linear model: A Monte Carlo Simulations Study

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Open Journal of Statistics 2020年第3期10卷 453-493页

作者： Oluwafemi Clement Onifade Samuel Olayemi Olanrewaju Department of Statistics Faculty of Science University of Abuja Abuja Nigeria

In a linear regression model, testing for uniformity of the variance of the residuals is a significant integral part of statistical analysis. This is a crucial assumption that requires statistical confirmation via the use of some statistical tests mostly before carrying out the Analysis of Variance (ANOVA) technique. Many academic researchers have published series of papers (articles) on some tests for detecting variance heterogeneity assumption in multiple linear regression models. So many comparisons on these tests have been made using various statistical techniques like biases, error rates as well as powers. Aside comparisons, modifications of some of these statistical tests for detecting variance heterogeneity have been reported in some literatures in recent years. In a multiple linear regression situation, much work has not been done on comparing some selected statistical tests for homoscedasticity assumption when linear, quadratic, square root, and exponential forms of heteroscedasticity are injected into the residuals. As a result of this fact, the present study intends to work extensively on all these areas of interest with a view to filling the gap. The paper aims at providing a comprehensive comparative analysis of asymptotic behaviour of some selected statistical tests for homoscedasticity assumption in order to hunt for the best statistical test for detecting heteroscedasticity in a multiple linear regression scenario with varying variances and levels of significance. In the literature, several tests for homoscedasticity are available but only nine: Breusch-Godfrey test, studentized Breusch-Pagan test, White’s test, Nonconstant Variance Score test, Park test, Spearman Rank, Glejser test, Goldfeld-Quandt test, Harrison-McCabe test were considered for this study;this is with a view to examining, by Monte Carlo simulations, their asymptotic behaviours. However, four different forms of heteroscedastic structures: exponential and linear (ge

关键词： Homoscedasticity Heteroscedasticity generalized linear model Monte Carlo

Approximate Conditional Likelihood for generalized linear models with General Missing Data Mechanism

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Journal of Systems Science & Complexity 2017年第1期30卷 139-153页

作者： ZHAO Jiwei SHAO Jun Department of Biostatistics State University of New York at Buffalo School of Statistics East China Normal University

The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and *** this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.

关键词： Asymptotic normality generalized linear model identifiability missing data mechanism,non-canonical link function nonignorable missingness.

Empirical Likelihood for generalized linear models with Longitudinal Data

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Journal of Systems Science & Complexity 2023年第5期36卷 2100-2124页

作者： YIN Changming AI Mingyao CHEN Xia KONG Xiangshun School of Mathematics and Information Science Guangxi UniversityNanning 530004China LMAM School of Mathematical Sciences and Center for Statistical SciencePeking UniversityBeijing 100871China School of Mathematics and Statistics Shaanxi Normal UniversityXi'an 710062China School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

generalized linear models are usually adopted to model the discrete or nonnegative *** this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is *** some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also *** with the existing results,the new conditions are more weak and easy to *** simulations are presented to illustrate these asymptotic properties.

关键词： Empirical likelihood ratio generalized linear model longitudinal data maximum empirical likelihood estimator

modeling effects of abiotic factors on the abundances of eight woody species in the Harana forest using artificial networks,random forest,and generalized linear models

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Ecological Processes 2023年第1期12卷 151-164页

作者： Girma Ayele Bedane Gudina Legese Feyisa Feyera Senbeta Wakjira Center for Environmental Science College of Computational and Natural ScienceAddis Ababa UniversityP.O.Box 1176Addis AbabaEthiopia Centre for Environment and Development College of Development StudiesAddis Ababa UniversityAddis AbabaEthiopia

Background Abiotic factors exert different impacts on the abundance of individual tree species in the forest but little has been known about the impact of abiotic factors on the individual plant,particularly,in a tropical *** study identified the impact of abiotic factors on the abundances of Podocarpus falcatus,Croton macrostachyus,Celtis africana,Syzygium guineense,Olea capensis,Diospyros abyssinica,Feliucium decipenses,and Coffea arabica.A systematic sample design was used in the Harana forest,where 1122 plots were established to collect the abundance of *** forest(RF),artificial neural network(ANN),and generalized linear model(GLM)models were used to examine the impacts of topographic,climatic,and edaphic factors on the log abundances of woody *** RF model was used to predict the spatial distribution maps of the log abundances of each *** The RF model achieved a better prediction accuracy with R^(2)=71%and a mean squared error(MSE)of 0.28 for Feliucium *** RF model differentiated elevation,temperature,precipitation,clay,and potassium were the top variables that influenced the abundance of *** ANN model showed that elevation induced a nega-tive impact on the log abundances of all woody *** GLM model reaffirmed the negative impact of elevation on all woody species except the log abundances of Syzygium guineense and Olea *** ANN model indicated that soil organic matter(SOM)could positively affect the log abundances of all woody *** GLM showed a similar positive impact of SOM,except for a negative impact on the log abundance of Celtis africana at p<*** spatial distributions of the log abundances of Coffee arabica,Filicium decipenses,and Celtis africana were confined to the eastern parts,while the log abundance of Olea capensis was limited to the western *** The impacts of abiotic factors on the abundance of woody species may vary with *** ecological underst

关键词： Species distribution model Random forest Artificial neural network generalized linear model Species abundance Woody species Environmental variable

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Sequential Feature Screening for generalized linear models with Sparse Ultra-High Dimensional Data

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Journal of Systems Science & Complexity 2020年第2期33卷 510-526页

作者： ZHANG Junying WANG Hang ZHANG Riquan ZHANG Jiajia Department of Mathematics Taiyuan University of TechnologyTaiyuan 030024China Department of Statistics East China Normal UniversityShanghai 200241China Department of Epidemiology and Biostatistics University of South CarolinaColumbia 20295USA

This paper considers the iterative sequential lasso(ISLasso)variable selection for generalized linear model with ultrahigh dimensional feature *** ISLasso selects features by estimated parameter sequentially iteratively for the second order approximation of likelihood function where the features selected depend on regulatory *** procedure stops when extended BIC(EBIC)reaches a *** study demonstrates that the new method is a desirable approach over other methods.

关键词： Extended BIC generalized linear model sequential lasso sequential iteration variable screening variable selection

ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN generalized linear modelS

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Chinese Annals of Mathematics,Series B 2005年第3期26卷 467-474页

作者： YUELI CHENXIRU SchoolofMathematicsandStatistics WuhanUniversityWuhan430072China GraduateSchooloftheChineseAcademyofSciences Beijing100049China

For the generalized linear model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.

关键词： Quasi likelihood estimate generalized linear model Asmptotically normal Asymptotic normality

Quasi-Maximum Likelihood Estimators in generalized linear models with Autoregressive Processes

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Acta Mathematica Sinica,English Series 2014年第12期30卷 2085-2102页

作者： Hong Chang HU Lei SONG School of Mathematics and Statistics Hubei Normal University Educational Research Institute

The paper studies a generalized linear model（GLM）yt = h（xt^T β）＋ εt,t = l,2,...,n,where ε1 = η1,ε1 =ρεt ＋ηt,t = 2,3,...;n,h is a continuous differentiable function,ηt＇s are independent and identically distributed random errors with zero mean and finite variance σ^***,the quasi-maximum likelihood（QML） estimators of β,p and σ^2 are ***,under mild conditions,the asymptotic properties（including the existence,weak consistency and asymptotic distribution） of the QML estimators are ***,the validity of method is illuminated by a simulation example.

关键词： generalized linear model quasi-maximum likelihood estimator autoregressive processes weak consistency asymptotic distribution