A finite mixture model using the Student's t distribution has been recognized as a robust extension of normal mixtures. Recently, a mixture of skew normal distributions has been found to be effective in the treatment of heterogeneous data involving asymmetric behaviors across subclasses. In this article, we propose a robust mixture framework based on the skew t distribution to efficiently deal with heavy-tailedness, extra skewness and multimodality in a wide range of settings. Statistical mixture modeling based on normal, Student's t and skew normal distributions can be viewed as special cases of the skew t mixture model. We present analytically simple EM-type algorithms for iteratively computing maximum likelihood estimates. The proposed methodology is illustrated by analyzing a real data example

The study of non-linear time series has attracted much attention in recent years. Among the models proposed, the threshold autoregressive (TAR) model and bilinear model are perhaps the most popular ones in the literature. However, the T A R model has not been widely used in practice due to the difficulty in identifying the threshold variable and in estimating the associated threshold value. The main focal point of this paper is a Bayesian analysis of the T A R model with two regimes. The desired marginal posterior densities of the threshold value and other parameters are obtained via the Gibbs sampler. This approach avoids sophisticated analytical and numerical multiple integration. It also provides an estimate of the threshold value directly without resorting to a subjective choice from various scatterplots. We illustrate the proposed methodology by using simulation experiments and analysis of a real data set.

This paper extends the classical linear mixed model by considering a multivariate skew-normal assumption for the distribution of random effects. We present an efficient hybrid ECME-NR algorithm for the computation of maximum-likelihood estimates of parameters. A score test statistic for testing the existence of skewness preference among random effects is developed. The technique for the prediction of future responses under this model is also investigated. The methodology is illustrated through an application to Framingham cholesterol data and a simulation study.

We discuss a robust extension of linear mixed models based on the multivariate t distribution. Since longitudinal data are successively collected over time and typically tend to be auto-correlated, we employ a parsimonious first-order autoregressive dependence structure for the within-subject errors. A score test statistic for testing the existence of autocorrelation among the within-subject errors is derived. Moreover, we develop an explicit scoring procedure for the maximum likelihood estimation with standard errors as a by-product. The technique for predicting future responses of a subject given past measurements is also investigated. Results are illustrated with real data from a multiple sclerosis clinical trial.