Misturas de regressões t de Student assimétricas com número de componentes desconhecido: uma aplicação do Telescoping Sampler

Abstract

Mixture models are suitable in situations where there is unobservable heterogeneity in the population. Commonly, the number of components present in the mixture is not known, one way to determine it is by using model selection criteria. In a Bayesian context, the estimation of the parameters of each component alongside the number of components is possible, several algorithms have been proposed for this end. The elescoping Sampler (TS) is a new alternative for the simultaneous estimation of the number of components and parameters in a Bayesian context. In regression analysis, the assumption of normality of observation errors is usually made. We extend this assumption by considering errors distributed according to a mixture of Skew-t distributions, thus comprising data with latent subgroups, skewness and the presence of outliers. In what follows, we present the TS and the mixture of Skew-t regressions, we investigate the parameter estimation of the regression mixture model using simulated data and fit the proposed model to a dataset comprising of baseball player salaries and measures of their in-game performance. The TS algorithm was able to recover the number of components and parameters fixed for the simulation and we see that the estimates of the regression coefficients in the regression mixture model are consistent.