This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

The generalized estimating equation (GEE) has been a popular tool for marginal regression analysis with longitudinal data, and its extension, the weighted GEE approach, can further accommodate data that are missing at random (MAR). Model selection methodologies for GEE, however, have not been systematically developed to allow for missing data. We propose the missing longitudinal information cri...

This paper proposes a data-driven approach that derives individual-specific sparse working correlation matrices for generalized estimating equations (GEEs). The approach is motivated by the observation that, in some applications of the GEE, the covariance structure across individuals is heterogeneous and cannot be appropriately captured by a single correlationmatrix. The proposed approach enjoy...

Selecting an appropriate working correlation structure is pertinent to clustered data analysis using generalized estimating equations (GEE) because an inappropriate choice will lead to inefficient parameter estimation. We investigate the well-known criterion of QIC for selecting a working correlation structure, and have found that performance of the QIC is deteriorated by a term that is theoret...

We consolidate the zero-inflated Poisson model for count data with excess zeros (Lambert, 1992) and the two-component model approach for serial correlation among repeated observations (Dobbie and Welsh, 2001) for spatial count data. This concurrently addresses the problem of overdispersion and distinguishes zeros that arise due to random sampling from those that arise due to inherent characteri...

A number of statistical methods are now available to map quantitative trait loci (QTL) relative to markers. However, no existing methodology can simultaneously map QTL for multiple nonnormal traits. In this article we rectify this deficiency by developing a QTL-mapping approach based on generalized estimating equations (GEE). Simulation experiments are used to illustrate the application of the ...

The Generalized Estimating Equations (GEE) is an approach to analyze correlated data. It is applied here to data from an epidemiological study of oesophageal cancer in a high incidence area in China to investigate familial aggregation. Regression diagnostics for mean structures and association structures are used to identify families that influence estimates of these structures. It is shown tha...

background: the celebrated generalized estimating equations (gee) approach is often used in longitudinal data analysis. while this method behaves robustly against misspecification of the working correlation structure, it has some limitations on efficacy of estimators, goodness-of-fit tests and model selection criteria. the quadratic inference functions (qif) is a new statistical methodology tha...

The generalized estimating equation (GEE) approach of Zeger and Liang facilitates analysis of data collected in longitudinal, nested, or repeated measures designs. GEEs use the generalized linear model to estimate more efficient and unbiased regression parameters relative to ordinary least squares regression in part because they permit specification of a working correlation matrix that accounts...

The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show ...