Modelling Conditional Densities Using Finite Smooth Mixtures

Smooth mixtures, i.e. mixture models with covariate-dependent mixing weights,are very useful flexible models for conditional densities. Previous work shows that using toosimple mixture components for modeling heteroscedastic and/or heavy tailed data can givea poor fit, even with a large number of components. This paper explores how well a smoothmixture of symmetric components can capture skewed data. Simulations and applications onreal data show that including covariate-dependent skewness in the components can lead tosubstantially improved performance on skewed data, often using a much smaller number ofcomponents. Furthermore, variable selection is effective in removing unnecessary covariates inthe skewness, which means that there is little loss in allowing for skewness in the componentswhen the data are actually symmetric. We also introduce smooth mixtures of gamma andlog-normal components to model positively-valued response variables