Relatórios de Pesquisa

7/2017 Likelihood-based Inference for Zero-or-one Augmented Rectangular Beta Regression Models
Ana R.S. Santos, Caio L. N. Azevedo, Jorge L. Bazan, Juvêncio S. Nobre

A new zero-and/or-one augmented beta rectangular regression model is introduced in this work, which is based on a new parameterization of the rectangular beta distribution. Maximum likelihood estimation is performed by using a combination of the EM algorithm (for the continuous part) and Fisher scoring algorithm (for discrete part). Also, we develop techniques of model t assessment, by using the randomized quantile residuals and model selection, considering criteria, such as AIC and BIC.We conducted several simulation studies, considering some situations of practical interest, in order to evaluate the parameter recovery of the proposed model and estimation method, the impact of transforming the observed zeros and ones with the use of non-augmented models and the behavior of the model selection criteria. A psychometric real data set was analyzed to illustrate the performance of the new approach considering the model studied.

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6/2017 Bayesian Inference for a Birnbaum-Saunders Regression Model Based on the Centered Skew Normal Distribution
Nathalia L. Chaves, Caio L N Azevedo, Filidor Vilca-Labra and Juvêncio S. Nobre
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5/2017 A Copula Based Modeling for Longitudinal IRT Data with Skewed Latent Distributions
José Roberto Silva dos Santos, Caio Lucidius Naberezny Azevedo
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4/2017 Bayesian General Cholesky Decomposition Based Modeling of Longitudinal Multiple-Group IRT Data with Skewed Latent Distributions and Growth Curves
José Roberto Silva dos Santos , Caio Lucidius Naberezny Azevedo
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3/2017 A General Cholesky Decomposition Based Modeling of Longitudinal IRT Data: Handling Skewed Latent Traits Distributions
José Roberto Silva dos Santos, Caio Lucidius Naberezny Azevedo
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2/2017 A General Cholesky Decomposition Based Modeling of Longitudinal IRT Data.
José Roberto Silva dos Santos, Caio Lucidius Naberezny Azevedo
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1/2017 Counting Numerical Semigroups by Genus and Even Gaps
Matheus Bernardini, Fernando Torres

We present an approach to count numerical semigroups of a given genus by using even gaps. Our method is motivated by the interplay between double covering of curves and γ-hyperelliptic semigroups [15], [12], [28], [18], [17].

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17/2016 On the curve Y^n = X^l (X^m + 1) over finite fields
Saeed Tafazolian, Fernando Torres

Let X be the nonsingular model of a plane curve of type y^n = f (x) over the finite field F of order q^2 , where f(x) is a separable polynomial of degree coprime to n. If the number of F-rational points of X attains the Hasse-Weil bound, then the condition n divides q + 1 is equivalente to the solubility of f(x) in F. In this paper, we investigate this condition for f(x) = x^l (x^m + 1)

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16/2016 On the spectrum for the genera of maximal curves over small fields
Nazar Arakelian, Saeed Tafazolian, Fernando Torres

Motivated by previous computations in Garcia, Stichtenoth and Xing (2000) paper [9], we discuss the spectrum M(q 2 ) for the genera of maximal curves over finite fields of order q 2 with 7 ≤ q ≤ 16. In particular, by using a result in Kudo and Harashita(2016) paper [17], the set M(7 2 ) is completely determined.

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15/2016 Finite mixture modeling of censored data using the multivariate Student-t distribution
Víctor H. Lachos, Edgar J. López Moreno, Kun Chen

Finite mixture models have been widely used for the modelling and analysis of data froma heterogeneous population. Moreover, these kind of data can be subjected to some upper and/or lower detection limits because of the restriction of experimental apparatus. Another complication arises when measures of each population depart significantly from normality, for instance, in the presence of heavy tails or atypical observations. For such data structures, we propose a robust model for censored data based on finite mixtures of multivariate Student-t distributions. This approach allows us to model data with great flexibility, accommodating multimodality, heavy tails and also skewness depending on the structure of the mixture components. We develop an analytically simple yet efficient EM-type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the multivariate truncated Student-t distributions. Further, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real data sets are reported to demonstrate the effectiveness of the proposed methodology. The proposed algorithm and methods are implemented in the new R package CensMixReg.

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