Joint GEEs for multivariate correlated data with incomplete binary outcomes

This study considers a fully-parametric but uncongenial multiple imputation (MI) inference to jointly analyze incomplete binary response variables observed in a correlated data settings. Multiple imputation model is specified as a fully-parametric model based on a multivariate extension of mixed-effects models. Dichotomized imputed datasets are then analyzed using joint GEE models where covariates are associated with the marginal mean of responses with response-specific regression coefficients and a Kronecker product is accommodated for cluster-specific correlation structure for a given response variable and correlation structure between multiple response variables. The validity of the proposed MI-based JGEE (MI-JGEE) approach is assessed through a Monte Carlo simulation study under different scenarios. The simulation results, which are evaluated in terms of bias, mean-squared error, and coverage rate, show that MI-JGEE has promising inferential properties even when the underlying multiple imputation is misspecified. Finally, Adolescent Alcohol Prevention Trial data are used for illustration.     

Estimation and diagnostic for skew-normal partially linear models

Partially linear models (PLMs) are an important tool in modelling economic and biometric data and are considered as a flexible generalization of the linear model by including a nonparametric component of some covariate into the linear predictor. Usually, the error component is assumed to follow a normal distribution. However, the theory and application (through simulation or experimentation) often generate a great amount of data sets that are skewed. The objective of this paper is to extend the PLMs allowing the errors to follow a skew-normal distribution [A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178], increasing the flexibility of the model. In particular, we develop the expectation-maximization (EM) algorithm for linear regression models and diagnostic analysis via local influence as well as generalized leverage, following [H. Zhu and S. Lee, Local influence for incomplete-data models, J. R. Stat. Soc. Ser. B 63 (2001), pp. 111–126]. A simulation study is also conducted to evaluate the efficiency of the EM algorithm. Finally, a suitable transformation is applied in a data set on ragweed pollen concentration in order to fit PLMs under asymmetric distributions. An illustrative comparison is performed between normal and skew-normal errors.     

Tests for Structural Changes in Time Series of Counts

We propose methods for detecting structural changes in time series with discrete‐valued observations. The detector statistics come in familiar L2‐type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data example.     

Marginal models for the association structure of hierarchical binary responses

Clustered binary responses are often found in ecological studies. Data analysis may include modeling the marginal probability response. However, when the association is the main scientific focus, modeling the correlation structure between pairs of responses is the key part of the analysis. Second-order generalized estimating equations (GEE) are established in the literature. Some of them are more efficient in computational terms, especially facing large clusters. Alternating logistic regression (ALR) and orthogonalized residual (ORTH) GEE methods are presented and compared in this paper. Simulation results show a slightly superiority of ALR over ORTH. Marginal probabilities and odds ratios are also estimated and compared in a real ecological study involving a three-level hierarchical clustering. ALR and ORTH models are useful for modeling complex association structure with large cluster sizes.     

Slashed generalized exponential distribution

In this paper, we introduce an extension of the generalized exponential (GE) distribution, making it more robust against possible influential observations. The new model is defined as the quotient between a GE random variable and a beta-distributed random variable with one unknown parameter. The resulting distribution is a distribution with greater kurtosis than the GE distribution. Probability properties of the distribution such as moments and asymmetry and kurtosis are studied. Likewise, statistical properties are investigated using the method of moments and the maximum likelihood approach. Two real data analyses are reported illustrating better performance of the new model over the GE model.     

Copulas related to piecewise monotone functions of the interval and associated processes

In this work, we derive the copulas related to vectors obtained from the so-called chaotic stochastic processes. These are defined by the iteration of certain piecewise monotone functions of the interval [0, 1] to some initial random variable. We study some of its properties and present some examples. Since often these types of copulas do not have closed formulas, we provide a general approximation method which converges uniformly to the true copula. Our results cover a wide class of processes, including the so-called Manneville–Pomeau processes. The general theory is applied to the parametric estimation in certain chaotic processes. A Monte Carlo simulation study is also presented.     

A general long-term aging model with different underlying activation mechanisms: Modeling,Bayesian estimation,and case influence diagnostics

In this paper we propose a general cure rate aging model. Our approach enables different underlying activation mechanisms which lead to the event of interest. The number of competing causes of the event of interest is assumed to follow a logarithmic distribution. The model is parameterized in terms of the cured fraction which is then linked to covariates. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis for the proposed model. Moreover, some discussions on the model selection to compare the fitted models are given, as well as case deletion influence diagnostics are developed for the joint posterior distribution based on the ψ-divergence, which has several divergence measures as particular cases, such as the Kullback–Leibler (K-L), J-distance, L₁ norm, and χ²-square divergence measures. Simulation studies are performed and experimental results are illustrated based on a real malignant melanoma data.     

Slashed generalized Rayleigh distribution

We introduce a new family of distributions suitable for fitting positive data sets with high kurtosis which is called the Slashed Generalized Rayleigh Distribution. This distribution arises as the quotient of two independent random variables, one being a generalized Rayleigh distribution in the numerator and the other a power of the uniform distribution in the denominator. We present properties and carry out estimation of the model parameters by moment and maximum likelihood (ML) methods. Finally, we conduct a small simulation study to evaluate the performance of ML estimators and analyze real data sets to illustrate the usefulness of the new model.