Full text
| |
| Author(s): |
Renata Guimarães Romeiro
Total Authors: 1
|
| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2018-10-05 |
| Examining board members: |
Filidor Edilfonso Vilca Labra;
Caio Lucidius Naberezny Azevedo;
Helton Saulo Bezerra dos Santos;
Edwin Moises Marcos Ortega;
Gilberto Alvarenga Paula
|
| Advisor: | Filidor Edilfonso Vilca Labra |
| Abstract | |
In this work, we propose a multivariate extension of the Birnbaum-Saunders (BS) distribution proposed by Kundu et al. (2010), based on scale-mixture of normal (SMN) distributions, used to model symmetric data. The resulting distribution will be called multivariate scale-mixture BS distribution (SBS). We will also consider other important approaches that have received consider- able attention in the literature, such as the regression models associated with the BS distribution and a study of diagnostic analysis Thus, considering the logarithmic transformation of the re- sponse variable with SBS distribution, we developed the sinh-SMN regression model, based on the works of Kundu (2015) and Vilca et al. (2014). This regression model can be seen as a robust multivariate extension, which is based on SMN distribution, of the regression model proposed by Rieck and Nedelman (1991). Due to the complexity of the likelihood of the model, and the direct maximization for parameter estimation, we explore a hierarchical representation and propose the estimation of maximum likelihood via an EM algorithm. We then developed two diagnostic anal- ysis approaches for the sinh-SMN regression model, considering the case exclusion (Cook 1977) of one or more observations, and a more general method proposed by Cook (1986). Finally, to evaluate the ability of the proposed methods, we performed simulation studies and analysis of real data (AU) | |
| FAPESP's process: | 13/25935-2 - Bivariate regression model Birnbaum-Saunders |
| Grantee: | Renata Guimarães Romeiro Agostinho |
| Support Opportunities: | Scholarships in Brazil - Doctorate |