- Prof. Víctor Leiva – Dep. Estadística, CIMFAV – Universidad de Valparaíso / Prof. Tomas Goicoa – Dep. Estadística e Investigación Operativa – Universidad Pública de Navarra, Espanha
- FCUL (DEIO) Campo Grande – Bloco C6 Piso 4 – Sala 6.4.30 – 14h
- Sexta-feira, 2 de Julho de 2010
Birnbaum and Saunders (1969) developed an interesting statistical distribution for modeling fatigue life. Birnbaum-Saunders (BS) models have largely been applied in engineering to relate the total time until failure with some type of cumulative damage (assumed to follow a normal distribution) caused by stress. Due to the theoretical arguments used for constructing this distribution, it is natural to find applications in other areas, such as actuarial science, medicine and environment. Even if this theoretical justification does not exist, the BS distribution can be used for fitting skewed data, such as it occurs with other well-known distributions, as the gamma, inverse Gaussian, lognormal and Weibull ones. In all these distributions, including the BS one, parameter estimates based on the maximum likelihood method are in general sensitive to atypical data. Díaz-García and Leiva (2005) proposed a general class of BS type distributions with good properties, where robust parameter estimation in presence of atypical data can be highlighted. Later, BS type regression models and their diagnostics were developed. In this talk, the BS distribution and its characterization and estimation, as well as some ideas on BS regression models, will be presented. In addition, a class of generalized BS distributions will be introduced. Finally, some applications based on censored and uncensored real data will be analyzed supported by an R package called gbs; see R Development Core Team (2009) and Leiva, Barros and Paula (2009). Robust and influence diagnostics aspects and the use of the EM algorithm will be also discussed; Balakrishnan, Leiva, Sanhueza and Vilca (2009).
Abstract: Seminar 2
A very important area of research in disease mapping is to study the temporal evolution of the geographical distribution of mortality (or incidence) risks. It helps to understand the risk factors involved in the disease, and to address important epidemiological questions about the stability of the estimated patterns of disease. Risk smoothing has been traditionally carried out using conditional autoregressive models but very recently, penalized splines have also been considered in an empirical Bayes spatial context. In this work, penalized splines for smoothing risks in both the spatial and the temporal dimensions will be applied. The mean squared error of the log-risk predictor are derived using ideas from the small area estimation literature allowing for constructing confidence intervals for the risks. To illustrate the procedure mortality data due to brain cancer in continental Spain over the period 1996-2005 are analyzed.