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Estimating Equations for Estimation of Mcdonald Generalized Beta— Binomial Parameters

Open Journal of Statistics 2014年第9期4卷 702-709页

作者： Nthiwa M. Janiffer Ali Islam Orawo Luke Department of Mathematics Egerton University Njoro Kenya

There has been a considerable recent attention in modeling over dispersed binomial data occurring in toxicology, biology, clinical medicine, epidemiology and other similar fields using a class of Binomial mixture distribution such as Beta Binomial distribution (BB) and Kumaraswamy-Binomial distribution (KB). A new three-parameter binomial mixture distribution namely, McDonald Generalized Beta Binomial (McGBB) distribution has been developed which is superior to KB and BB since studies have shown that it gives a better fit than the KB and BB distribution on both real life data set and on the extended simulation study in handling over dispersed binomial data. The dispersion parameter will be treated as nuisance in the analysis of proportions since our interest is in the parameters of McGBB distribution. In this paper, we consider estimation of parameters of this MCGBB model using quasi-likelihood (QL) and Quadratic estimating functions (QEEs) with dispersion. By varying the coefficients of the QEE’s we obtain four sets of estimating equations which in turn yield four sets of estimates. We compare small sample relative efficiencies of the estimates based on QEEs and quasi-likelihood with the maximum likelihood estimates. The comparison is performed using real life data sets arising from alcohol consumption practices and simulated data. These comparisons show that estimates based on optimal QEEs and QL are highly efficient and are the best among all estimates investigated.

关键词： Maximum likelihood McDonald Generalized Beta Binomial Simulation Quadratic Estimating Equations quasi-likelihood

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Estimation and Inference for Proportional Response Cluster Data with Partially Linear Additive Model

Estimation and Inference for Proportional Response Cluster D...

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第十届海峡两岸统计与概率研讨会

作者： Weihua Zhao Nantong University

Proportional data with support lying in the interval [0,1] are frequently analyzed in medicine and public health. When the data is collected by cluster, it is important to correct-ly incorporate the correlations within cluster to improve estimation e ciency. In this paper, we investigate the proportional cluster response data with partially linear additive model based on quadratic inference function(QIF). By borrowing the quasi- likelihood estimation method of Pap-ke and Wooldridge(1996) and the polynomial splines approximation for unknown nonparametric functions, we obtain the estimators for both parametric part and nonparametric part and their large sample theoretical properties are also established. Extensive simulation studies are used to illustrate the usefulness of the proposed method, which is more e cient than the simple estimate without incorporating the correlations. Finally, we apply the new method to a clinical periodon-tology study.

关键词： Proportional data Cluster data quasi-likelihood Quadratic inference function Within-cluster correlation

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