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ITERATIVE quasi-likelihood FOR SEEMINGLY UNRELATED REGRESSION SYSTEMS

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Chinese Annals of Mathematics,Series B 2005年第3期26卷 335-346页

作者： LINLU FANYUNZHENG DUJUN YUANYUAN SchoolofMathematicsandSystemSciences ShandongUniversityJinan250100ShandongChina. SchoolofMathematicsandSystemSciences ShandongUniversityJinan250100ShandongChina／／DepartmentofMathematicsNantongUniversityNantong226007JiangsuChina. SchoolofMathematicalSciences NankaiUniversityTianjin300071China. ProjectsupportedbytheNationalNaturalScienceFoundationofChina

In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating *** finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.

关键词： Seemingly unrelated regression system quasi-likelihood Unbiased estimating function

Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

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Science China Mathematics 2006年第2期49卷 145-157页

作者： YIN Changming, ZHAO Lincheng & WEI Chengdong School of Mathematics and Information Science, Guangxi University, Manning 530004, China Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China Department of Mathematics, Guangxi Teacher College, Manning 530001, China School of Mathematics and Information Science Guangxi University Nanning China Department of Statistics and Finance University of Science and Technology of China Hefei China Department of Mathematics Guangxi Teacher College Nanning China

In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.

关键词： generalized linear models quasi-likelihood estimates asymptotic normality strong consistency.

Two-step Estimation for Longitudinal Data When the Working Correlation Matrix is a Linear Combination of Some Known Matrices

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Acta Mathematicae Applicatae Sinica 2019年第2期35卷 264-273页

作者： Yu-ling LI Wei GAO Man-Lai TANG Shu-rong ZHENG Key Laboratory for Applied Statistics of MOE School of Mathematics and StatisticsNortheast Normal University School of Applied Mathematics Beijing Normal University Department of Mathematics and Statistics Hang Seng Management College

The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification, the corresponding efficiency can be severely affected. In this paper, we propose a new two-step estimation method in which the correlation matrix is assumed to be a linear combination of some known working matrices. Asymptotic properties of the new estimators are *** studies are conducted to examine the performance of the proposed estimators. We illustrate the methodology with an epileptic data set.

关键词： generalized estimating equations longitudinal data quadratic inference functions quasi-likelihood two-step estimation

Statistical inference for right-censored data with nonignorable missing censoring indicators

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Science China Mathematics 2013年第6期56卷 1263-1278页

作者： SUN ZhiHua XIE TianFa LIANG Hua School of Mathematical Sciences University of Chinese Academy of Sciences College of Applied Sciences Beijing University of Technology Department of Biostatistics and Computational Biology University of RochesterRochester NY 14642 USA

We consider the statistical inference for right-censored data when censoring indicators are missing but nonignorable, and propose an adjusted imputation product-limit estimator. The proposed estimator is shown to be consistent and converges to a Gaussian process. Furthermore, we develop an empirical processbased testing method to check the MAR (missing at random) mechanism, and establish asymptotic properties for the proposed test statistic. To determine the critical value of the test, a consistent model-based bootstrap method is suggested. We conduct simulation studies to evaluate the numerical performance of the proposed method and compare it with existing methods. We also analyze a real data set from a breast cancer study for an illustration.

关键词： MAR mechanism testing nonignorable missing censoring indicators survival function quasi-likelihood

Stochastic loss reserving using individual information model with over-dispersed Poisson

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Statistical Theory and Related Fields 2022年第2期6卷 114-128页

作者： Zhigao Wang Xianyi Wu Chunjuan Qiu School of Statistics East China Normal UniversityShanghaiPeople’s Republic of China

For stochastic loss reserving,we propose an individual information model(IIM)which accom-modates not only individual/micro data consisting of incurring times,reporting developments,settlement developments as well as payments of individual claims but also heterogeneity among *** give over-dispersed Poisson assumption about the moments of reporting developments and payments of every individual *** estimation is conducted under quasi-likelihood *** expressions are derived for the expectation and variance of outstanding liabilities,given historical *** utilise conditional mean square error of prediction(MSEP)to measure the accuracy of loss reserving and also theoretically prove that when risk portfolio size is large enough,IIM shows a higher prediction accuracy than individ-ual/micro data model(IDM)in predicting the outstanding liabilities,if the heterogeneity indeed influences claims developments and otherwise IIM is asymptotically equivalent to *** simulations are conducted to investigate the conditional MSEPs for IIM and IDM.A real data analysis is performed basing on real observations in health insurance.

关键词： Risk management loss reserving individual information model over-dispersed Poisson quasi-likelihood MSEP

Maximum Entropy Empirical likelihood Methods Based on Laplace Transforms for Nonnegative Continuous Distribution with Actuarial Applications

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Open Journal of Statistics 2017年第3期7卷 459-482页

作者： Andrew Luong É cole d’actuariat Université Laval Ste Foy Québec Canada

Maximum entropy likelihood (MEEL) methods also known as exponential tilted empirical likelihood methods using constraints from model Laplace transforms (LT) are introduced in this paper. An estimate of overall loss of efficiency based on Fourier cosine series expansion of the density function is proposed to quantify the loss of efficiency when using MEEL methods. Penalty function methods are suggested for numerical implementation of the MEEL methods. The methods can easily be adapted to estimate continuous distribution with support on the real line encountered in finance by using constraints based on the model generating function instead of LT.

关键词： quasi-likelihood Projection Power Mixture Operator Quadratic Distance Methods Insurance Premium Stop-Loss Premium

Bootstrap Confidence Intervals for Proportions of Unequal Sized Groups Adjusted for Overdispersion

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Open Journal of Statistics 2015年第6期5卷 502-510页

作者： Olivia Wanjeri Mwangi Ali Islam Orawo Luke Department of Mathematics Egerton University Njoro Kenya

Group testing is a method of pooling a number of units together and performing a single test on the resulting group. It is an appealing option when few individual units are thought to be infected leading to reduced costs of testing as compared to individually testing the units. Group testing aims to identify the positive groups in all the groups tested or to estimate the proportion of positives (p) in a population. Interval estimation methods of the proportions in group testing for unequal group sizes adjusted for overdispersion have been examined. Lately improvement in statistical methods allows the construction of highly accurate confidence intervals (CIs). The aim here is to apply group testing for estimation and generate highly accurate Bootstrap confidence intervals (CIs) for the proportion of defective or positive units in particular. This study provided a comparison of several proven methods of constructing CIs for a binomial proportion after adjusting for overdispersion in group testing with groups of unequal sizes. Bootstrap resampling was applied on data simulated from binomial distribution, and confidence intervals with high coverage probabilities were produced. This data was assumed to be overdispersed and independent between groups but correlated within these groups. Interval estimation methods based on the Wald, the Logit and Complementary log-log (CLL) functions were considered. The criterion used in the comparisons is mainly the coverage probabilities attained by nominal 95% CIs, though interval width is also regarded. Bootstrapping produced CIs with high coverage probabilities for each of the three interval methods.

关键词： Group Testing Overdispersion quasi-likelihood Confidence Interval Bootstrapping Coverage Probability

Unified Asymptotic Results for Maximum Spacing and Generalized Spacing Methods for Continuous Models

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Open Journal of Statistics 2018年第3期8卷 614-639页

作者： Andrew Luong école d’Actuariat Université Laval Québec Canada

Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.

关键词： Maximum Product of Spacings M-Estimators quasi-likelihood Ratio Test Statistic α-Mixing Sequences

Efficiency of Some Estimators for a Generalized Poisson Autoregressive Process of Order 1

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Open Journal of Statistics 2016年第4期6卷 637-650页

作者： Louis G. Doray Andrew Luong El-Halla Najem Département de Mathématiques et de Statistique Université de Montréal Montréal Canada école d’Actuariat Université Laval Québec Canada

Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.

关键词： Discrete Time Series Autoregressive Process Moment Estimator quasi-likelihood Efficiency Generalized Poisson quasi Binomial Distribution