We describe an extension of the hidden Markov model in which the manifest process conditionally follows a partition model. The assumption of local independence for the manifest random variable is thus relaxed to arbitrary dependence. The proposed class generalizes different existing models for...

We propose a simple estimator for the weight in a two-component mixture model between a known and an unknown density. We make no parametric assumptions about the unknown component and estimate the weight conservatively, i.e., the estimate is smaller than the true value with high probability. A...

We discuss an interpretation of the mixture transition distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be...

Multivariate outlier identification requires the choice of reliable cut-off points for the robust distances that measure the discrepancy from the fit provided by high-breakdown estimators of location and scatter. Multiplicity issues affect the identification of the appropriate cut-off points. It...

We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal data. The main assumption behind these models is that the response variables are conditionally independent given a latent process which follows a first-order Markov chain. We first illustrate the...

Robust distances are mainly used for the purpose of detecting multivariate outliers. The precise definition of cut-off values for formal outlier testing assumes that the “good” part of the data comes from a multivariate normal population. Robust distances also provide valuable information on...

<Para ID="Par1">A method for robust estimation of dynamic mixtures of multivariate distributions is proposed. The EM algorithm is modified by replacing the classical M-step with high breakdown S-estimation of location and scatter, performed by using the bisquare multivariate S-estimator. Estimates are obtained...</para>

A two-component parametric mixture is proposed to model survival after an invasive treatment, when patients may experience different hazards regimes: a risk of early mortality directly related to the treatment and/or the treated condition, and a risk of late death influenced by several exogenous...