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| Author(s): |
Ana Roberta dos Santos Silva
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2015-02-26 |
| Examining board members: |
Caio Lucidius Naberezny Azevedo;
Víctor Hugo Lachos Dávila;
Jorge Luis Bazán Guzmán
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| Advisor: | Caio Lucidius Naberezny Azevedo |
| Abstract | |
In this work we developed the zero-one augmented rectangular beta distribution, as well as a correspondent zero-one augmented rectangular beta regression model to analyze limited-augmented data (represented by mixed random variables with limited support), which present outliers. We develop inference tools under the Bayesian and frequentist approaches. Regarding to the Bayesian inference, due the impossibility of obtaining analytically the posterior distributions of interest, we used MCMC algorithms. Concerning the frequentist estimation, we use the EM algorithm. We develop techniques of residual analysis, by using the randomized quantile residuals, under both frequentist and Bayesian approaches. We also developed influence measures, only under the Bayesian approach, by using the measure of Kullback Leibler. In addition, we adapt methods of posterior predictive checking available in the literature, to our model, using appropriate discrepancy measures. For model selection, we use the criteria commonly employed in the literature, such as AIC, BIC and DIC. We performed several simulation studies, considering some situations of practical interest, in order to compare the Bayesian and frequentist estimates, as well as to evaluate the behavior of the developed diagnostic tools. A psychometric real data set was analyzed to illustrate the performance of the developed tools (AU) | |
| FAPESP's process: | 13/07850-0 - Zero-one heteroscedastic augmented rectangular beta regression models |
| Grantee: | Ana Roberta dos Santos Silva |
| Support Opportunities: | Scholarships in Brazil - Master |