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Parametric and semi-parametric regression models under the class of scale mixtures of normal distributions


Parametric and semi-parametric regression models represent two major areas in the modelingcontext, which have found applications in different areas. The aim of this project is to consider regression models in the presence of random effects,which are distributed under the family of scale mixture of skew-normal distributions (Branco and Dey 2001), that are effectively used in robust estimation in the presence of extreme observations.The main regression models that will be considered are: i) mixed linear model, ii) measurementerror model and iii) regression model of Item Response Theory (IRT).For the regression models (mixed linear model and measurement error model) uncensoredand for censored data, estimation and diagnostic analysis studies are considered, under parametricand semi-parametric structures. The semi-parametric regression refers to the flexibleincorporation of non-linear functional relationships into regression analysis. On the other hand,regression models in IRT, used more frequently in latent trait evaluations psychometric tests, theproposed models are based on asymmetric centered distributions. The estimation is consideredfrom a frequentist and Bayesian viewpoints. (AU)

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