A Weighting Approach for GEE Analysis with Missing Data

We propose a new weighting (WT) method to handle missing categorical outcomes in longitudinal data analysis using generalized estimating equations (GEE). The proposed WT provides a valid GEE estimator when the data are missing at random (MAR), and has more stable weights and shows advantage in efficiency compared to the inverse probability weighing method in the presence of small observation probabilities. The WT estimator is similar to the stabilized weighting (SWT) estimator under mild conditions, but it is more stable and efficient than SWT when the associations of the outcome with the observation probabilities and the covariate are strong.     

Joint Moment Generating Functions of Nonadjacent Dual Generalized Order Statistics from Reflected Generalized Pareto Distributions

In this article, a class of reflected generalized Pareto distributions (cf. Burkschat et al., 2003 Burkschat , M. , Cramer , E. , Kamps , U. ( 2003 ). Dual generalized order statistics . Metron LXI ( 1 ): 13 – 26 . [Google Scholar]) is considered. Recurrence relations for joint moment generating functions of higher non adjacent dual generalized order statistics based on a random sample drawn from the considered class are derived. Higher joint moments of non adjacent dual generalized order statistics (reversed ordered order statistics and lower k-records as special cases) are obtained. Recurrence relations for single and product moment generating functions and moments of higher non adjacent dual generalized order statistics are derived. Some results of higher moments of non adjacent generalized order statistics from generalized Pareto distributions (cf. Johnson et al., 1995 Johnson , N. L. , Kotz , S. , Balakrishnan , N. ( 1995 ). Continuous Univariate Distributions. , 2nd ed. Vol. 2. New York : Wiley & Sons . [Google Scholar]), are obtained by using a relation connecting higher moments of generalized order statistics and its dual.     

The Joint Distribution of the Sum and the Maximum of IID Exponential Random Variables

The authors establish the joint distribution of the sum X and the maximum Y of IID exponential random variables. They derive exact formuli describing the random vector (X, Y), including its joint PDF, CDF, and other characteristics; marginal and conditional distributions; moments and related parameters; and stochastic representations leading to further properties of infinite divisibility and self-decomposability. The authors also discuss parameter estimation and include an example from climatology that illustrates the modeling potential of this new bivariate model.     

A Lagrangian Non Central Negative Binomial Distribution of the First Kind

A Lagrangian probability distribution of the first kind is proposed. Its probability mass function is expressed in terms of generalized Laguerre polynomials or, equivalently, a generalized hypergeometric function. The distribution may also be formulated as a Charlier series distribution generalized by the generalizing Consul distribution and a non central negative binomial distribution generalized by the generalizing Geeta distribution. This article studies formulation and properties of the distribution such as mixture, dispersion, recursive formulas, conditional distribution and the relationship with queuing theory. Two illustrative examples of application to fitting are given.     

Generalized Jackknife-Based Estimators for Univariate Extreme-Value Modeling

In this article, we revisit the importance of the generalized jackknife in the construction of reliable semi-parametric estimates of some parameters of extreme or even rare events. The generalized jackknife statistic is applied to a minimum-variance reduced-bias estimator of a positive extreme value index—a primary parameter in statistics of extremes. A couple of refinements are proposed and a simulation study shows that these are able to achieve a lower mean square error. A real data illustration is also provided.     

On the Use of Semi-folding in Regular Blocked Two-level Factorial Designs

In this article, we consider experimental situations where a blocked regular two-level fractional factorial initial design is used. We investigate the use of the semi-fold technique as a follow-up strategy for de-aliasing effects that are confounded in the initial design as well as an alternative method for constructing blocked fractional factorial designs. A construction method is suggested based on the full foldover technique and sufficient conditions are obtained when the semi-fold yields as many estimable effects as the full foldover.     

A Compressive Sensing Based Analysis of Anomalies in Generalized Linear Models

In this article, we present a compressive sensing based framework for generalized linear model regression that employs a two-component noise model and convex optimization techniques to simultaneously detect outliers and determine optimally sparse representations of noisy data from arbitrary sets of basis functions. We then extend our model to include model order reduction capabilities that can uncover inherent sparsity in regression coefficients and achieve simple, superior fits. Second, we use the mixed ?₂/?₁ norm to develop another model that can efficiently uncover block-sparsity in regression coefficients. By performing model order reduction over all independent variables and basis functions, our algorithms successfully deemphasize the effect of independent variables that become uncorrelated with dependent variables. This desirable property has various applications in real-time anomaly detection, such as faulty sensor detection and sensor jamming in wireless sensor networks. After developing our framework and inheriting a stable recovery theorem from compressive sensing theory, we present two simulation studies on sparse or block-sparse problems that demonstrate the superior performance of our algorithms with respect to (1) classic outlier-invariant regression techniques like least absolute value and iteratively reweighted least-squares and (2) classic sparse-regularized regression techniques like LASSO.     

The Generalized Pascal Triangle and the Matrix Variate Jensen-Logistic Distribution

This article defines the so called Generalized Matrix Variate Jensen-Logistic distribution. The relevant applications of this class of distributions in Configuration Shape Theory consist of a more efficient computation, supported by the corresponding inference. This demands the solution of two important problems: (1) the development of analytical and efficient formulae for their k-th derivatives and (2) the use of the derivatives to transform the configuration density into a polynomial density under some special matrix Kummer relation, indexed in this case by the Jensen-Logistic kernel. In this article, we solve these problems by deriving a simple formula for the k-th derivative of the density function, avoiding the usual partition theory framework and using a generalization of Pascal triangles. Then we apply the results by obtaining the associated Jensen-Logistic Kummer relations and the configuration polynomial density in the setting of Statistical Shape Theory.     

Bonferroni-type Plug-in Procedure Controlling Generalized Familywise Error Rate

Consider the multiple hypotheses testing problem controlling the generalized familywise error rate k-FWER, the probability of at least k false rejections. We propose a plug-in procedure based on the estimation of the number of true null hypotheses. Under the independence assumption of the p-values corresponding to the true null hypotheses, we first introduce the least favorable configuration (LFC) of k-FWER for Bonferroni-type plug-in procedure, then we construct a plug-in k-FWER-controlled procedure based on LFC. For dependent p-values, we establish the asymptotic k-FWER control under some mild conditions. Simulation studies suggest great improvement over generalized Bonferroni test and generalized Holm test.     

Generalized Analysis-of-variance-type Test for the Single-index Quantile Model

In this paper, we are concerned with a test for the index parameter and index function in the single-index model. Based on the estimates obtained by the quantile regression, we extend the generalized analysis-of-variance-type test to the single-index model. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows an asymptotically χ²-distribution. The simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.