Validation and modeling of heteroscedastic and/or autoregressive structures in elliptical nonlinear models for correlated data

• Grant number: 09/14911-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2010
• End date: January 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Gilberto Alvarenga Paula
• Grantee: Cibele Maria Russo Novelli
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we propose the investigation of important issues related to the nonlinear mixed-effects modeling assuming elliptical errors, including the assumption of heteroscedastic and/or autoregressive structures as a generalization of the scale matrix from the models developed by the applicant Cibele Russo in her Doctorate Thesis and published in Computational Statistics and Data Analysis. The elliptical nonlinear models with mixed effects provide relevant alternatives for the modeling of longitudinal data, since it introduce the intragroup correlation and permit the obtaintion of robust estimates against aberrant observations and few sensitive to perturbations. However, a more sofisticated modeling on the involved scale matrix may provide a significative gain for the models when variability and dependence patterns among the measurements taken in the same experimental unit are observed. Moreover, validation and diagnostic techniques for the proposed models will be investigated, which provide important tools for the choice of models. The results will be applied to real data.