Multivariate Hidden Markov Regression Models with Random Covariates

Hidden Markov regression models with random covariates (HMRM RCs) are introduced with the aim of improving the recovering of the latent structure in the data with respect to a fixed covariates paradigm. To add flexibility to the proposed approach, HMRMRCs are defined focusing on three multivariate Gaussian scale mix ture distributions: the Gaussian (reference distribution), the t, and the contaminated Gaussian. The latter two distributions are introduced to protect the reference model for the occurrence of mildly atypical points and also allow for their automatic detec tion. These distributions give rise to a family of nine HMRMRCs. Real data analysis is provided to investigate models behavior in presence of heterogeneity and atypical observations.