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This paper discusses state-space models with multi-categorical longitudinal observations and states characterized by the so-called Conditional Heteroskedastic AutoRegressive Nonlinear (CHARN) models. The latter are estimated via generalized Kalman recursions based on particle filters and EM algorithm. Our findings generalize the literature. They are illustrated by numerical simulations and applied to data from patients surged for breast cancer.
In this paper, we present some parametric families of probability distributions associated to particular single type homogeneous branching processes in continuous time. Their simplicity and the relevance of the interpretation of parameters for many domains of applications are of valuable interest for statistical inference. These families are particularly well adapted to handle branching dynamical systems of populations where Poisson assumption is generally but mistakenly assumed. Calculations and pertinent properties concerning these probability distributions are derived from their generating functions satisfying specific linear partial differential equations. As a by product, these equations allow the statement of a general recurrence formula for factorial moments.
In this paper, we present a latent based method to model the longitudinal evolution of Health related quality of life of patients under specific survey conditions. First of all, we will deal with the frequent issue when different questionnaires are sequentially used to measure the same latent trait during a long follow up time. Secondly, we propose models allowing the latent process to potentially behave under a long range memory constraint as the quality of life of an individual can highly depend on his or her far antecedents. For that purpose, we constructed a general statistical framework and gave the corresponding likelihood formula. Then, we developed an approximation algorithm for the likelihood, within the R-software, and applied it to a real data set. The statistical results obtained for this data set substantiate the following points : The pertinence of this approach concerning some rational testing hypotheses, the compliance of the parameter estimate values as well as it robustness with respect to measurement protocol changes.
