A robust approach to joint modeling of mean and scale covariance for longitudinal data

In this paper, we propose a multivariate t$t$ regression model with its mean and scale covariance modeled jointly for the analysis of longitudinal data. A modified Cholesky decomposition is adopted to factorize the dependence structure in terms of unconstrained autoregressive and scale innovation parameters. We present three distinct representations of the log-likelihood function of the model and study the associated properties. A computationally efficient Fisher scoring algorithm is developed for carrying out maximum likelihood estimation. The technique for the prediction of future responses in this context is also investigated. The implementation of the proposed methodology is illustrated through two real-life examples and extensive simulation studies.     

Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects

Adaptive designs are sometimes used in a phase III clinical trial with the goal of allocating a larger number of patients to the better treatment. In the present paper we use some adaptive designs in a two-treatment two-period crossover trial in the presence of possible carry-over effects, where the treatment responses are binary. We use some simple designs to choose between the possible treatment combinations AA, AB, BA or BB. The goal is to use the better treatment a larger proportion of times. We calculate the allocation proportions to the possible treatment combinations and their standard deviations. We also investigate related inferential problems, for which related asymptotics are derived. The proposed procedure is compared with a possible competitor. Finally we use real data sets to illustrate the applicability of our proposed design.     

Some developments on the log-Dagum distribution

Skewed and fat-tailed distributions frequently occur in many applications. Models proposed to deal with skewness and kurtosis may be difficult to treat because the density function cannot usually be written in a closed form and the moments might not exist. The log-Dagum distribution is a flexible and simple model obtained by a logarithmic transformation of the Dagum random variable. In this paper, some characteristics of the model are illustrated and the estimation of the parameters is considered. An application is given with the purpose of modeling kurtosis and skewness that mark the financial return distribution.      

Separating the Harmful Versus Beneficial Effects of Marital Disruptions on Children

Although a marital disruption can certainly be harmful for some children, it might be beneficial to other children. Analyses on how children are affected by marital disruptions typically capture the average estimated effects (or associations) of a disruption on an outcome. Thus, the harmful effects of the disruption on some children are being averaged with the neutral and beneficial effects on other children. This could mute the estimated effect, and it could prevent the detection of significant harmful (or beneficial) effects. Using achievement test scores and an index of behavioral problems in a first-difference framework, I find evidence for the standard approach having muted estimated effects and failing to detect significant effects when the same data produce significant isolated harmful effects.     

Inference for a simple step-stress model with progressively censored competing risks data from Weibull distribution

In reliability analysis, it is common to consider several causes, either mechanical or electrical, those are competing to fail a unit. These causes are called “competing risks.” In this paper, we consider the simple step-stress model with competing risks for failure from Weibull distribution under progressive Type-II censoring. Based on the proportional hazard model, we obtain the maximum likelihood estimates (MLEs) of the unknown parameters. The confidence intervals are derived by using the asymptotic distributions of the MLEs and bootstrap method. For comparison, we obtain the Bayesian estimates and the highest posterior density (HPD) credible intervals based on different prior distributions. Finally, their performance is discussed through simulations.     

On several estimates to the precision parameter of Dirichlet process prior

The article presents careful comparisons among several empirical Bayes estimates to the precision parameter of Dirichlet process prior, with the setup of univariate observations and multigroup data. Specifically, the data are equipped with a two-stage compound sampling model, where the prior is assumed as a Dirichlet process that follows within a Bayesian nonparametric framework. The precision parameter α measures the strength of the prior belief and kinds of estimates are generated on the basis of observations, including the naive estimate, two calibrated naive estimates, and two different types of maximum likelihood estimates stemming from distinct distributions. We explore some theoretical properties and provide explicitly detailed comparisons among these estimates, in the perspectives of bias, variance, and mean squared error. Besides, we further present the corresponding calculation algorithms and numerical simulations to illustrate our theoretical achievements.     

Estimation du comportement asymptotique des autocovariances et autocorrelations empiriques de processus multivariéeas

Statistics based on the sample autocovariances are widely used in time-series analysis. Estimators of the asymptotic covariance between the sample autocovariances are commonly derived from the so-called Bartlett's formula. However, this formula essentially holds for linear processes. This entails that for a wide range of nonlinear time series the above-mentioned estimators are not suitable. In this paper the behaviour of an alternative estimator is studied within the framework of centered or uncentered multivariate strongly mixing processes. Applications to differential functions of sample autocovariances, such as the sample autocorrelations, are considered.     

具有混合边界条件的地下水污染模型的特征有限元方法

本文研究了地下水污染理论中的一类带混合边界条件的非线性耦合方程组的特征有限元方法，构造模型的特征有限元全离散格式，且利用椭圆投影，建立了计算格式在Ｈ＾１模下的最佳阶误差估计，并给出了数值算例及结果分析。