Zero-one heteroscedastic augmented rectangular beta regression models

• Grant number: 13/07850-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2013
• End date: February 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Caio Lucidius Naberezny Azevedo
• Grantee: Ana Roberta dos Santos Silva
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 12/21788-2 - Regression models and applications, AP.TEM

Abstract

Increasingly, in many knowledge fields, arise data sets with particular characteristics for which, in general, existence methodologies of statistical analysis, do not exist. Particularly, the using of regression model can be useful to answer the questions of interest. However, due to the aforementioned characteristics, usual assumptions such as: distribution of response variable, link function and shape of the predictor, can be not satisfied by the existen models in the literature related to these data sets. Particularly, when the chosen distribution for modelling response variable is not suitable, one can transform the data in order to be possible the using of some existence model. However, it is known that such approach can present some problems. On the other hand, sometimes it is possible to observe variables lying in the (0,1) plus 0 and 1 values, with positive probabilities. In other words, we have a mixture random variable. In this sense, the main goal of this project is to consider a heteroscedastic zero-one inflated triangular beta regression model. This model generalizes some works in the literature. We will propose estimation and residual analysis under both frequentist and bayesian paradigms. Also, we will study the obtaining and the using of the Jeffreys prior. In addition, some simulation studies will be considered in order to comparar the frequentist and bayesian approaches. Real data analysis will be also considered. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SILVA, ANA R. S.; AZEVEDO, CAIO L. N.; BAZAN, JORGE L.; NOBRE, JUVENCIO S.. Bayesian inference for zero-and/or-one augmented beta rectangular regression models. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 35, n. 4, p. 749-771, NOV 2021. (13/07850-0)

SILVA, ANA R. S.; AZEVEDO, CAIO L. N.; BAZAN, JORGE L.; NOBRE, JUVENCIO S.. Augmented-limited regression models with an application to the study of the risk perceived using continuous scales. Journal of Applied Statistics, v. 48, n. 11, p. 24-pg., 2020-06-30. (13/07850-0)

SILVA, ANA R. S.; AZEVEDO, CAIO L. N.; BAZAN, JORGE L.; NOBRE, JUVENCIO S.. Augmented-limited regression models with an application to the study of the risk perceived using continuous scales. Journal of Applied Statistics, JUN 2020. (13/07850-0)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SILVA, Ana Roberta dos Santos. Zero-one augmented heteroscedastic rectangular beta regression models. 2015. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.