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| Author(s): |
Christian Eduardo Galarza Morales
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2020-03-23 |
| Examining board members: |
Larissa Avila Matos;
Filidor Edilfonso Vilca Labra;
Silvia Lopes de Paula Ferrari;
Elcio Lebensztayn;
Clecio da Silva Ferreira
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| Advisor: | Víctor Hugo Lachos Dávila; Larissa Avila Matos |
| Abstract | |
In this thesis, we calculate doubly truncated moments, that is, in a hyper-rectangle, for a general class of asymmetric distributions called the selection elliptical family multivariate. This large family of distributions includes complex multivariate asymmetric versions of well-known elliptical distributions as the normal, Student’s t, exponential power, hyperbolic, Slash, Pearson type II, contaminated normal, among others. In four paper-based chapters, we present recurrent formulations for moments of doubly truncated and folded multivariate distributions, explicit expressions for particular cases as univariate lower order moments, sufficient and necessary conditions for the existence of truncated moments, comparison of computational efficiency between models, simulation studies, optimized approaches as well as numerical approximation for special cases such as limiting cases, and moments when a partition has almost zero volume or no truncation. Methods for performing estimation on censored skewed multivariate regression models are presented and showed through three real-life applications. Furthermore, general results for the scale-mixture of normal distributions are presented. The methods proposed have been implemented in the MomTrunc package of the R software, a highly optimized package including C++ routines through Rcpp, that offers theoretical, Monte Carlo truncated moments and other functions of interest as probability density, cumulative distribution, and random generator functions for various symmetric and asymmetric multivariate distributions. (AU) | |
| FAPESP's process: | 15/17110-9 - Robust Estimation in Spatial Models for Censored Data |
| Grantee: | Christian Eduardo Galarza Morales |
| Support Opportunities: | Scholarships in Brazil - Doctorate |