nÃo hà / Esta dissertaÃÃo tem por objetivo calcular as taxas de sobrevivÃncia dos participantes de Fundos de PensÃo do setor elÃtrico nacional, bem como encontrar o modelo paramÃtrico de sobrevivÃncia que melhor represente os dados em estudo. Para desenvolvimento do trabalho utilizamos dados de 14 entidades com informaÃÃes de participantes ativos e aposentados, com exceÃÃo dos invÃlidos, referentes ao perÃodo de 2001 a 2009, totalizando um nÃmero total de 100.000 vidas analisadas. Para calcular as taxas brutas de sobrevivÃncia, utilizamos o mÃtodo indireto, descrito em Ferreira (1985). ApÃs o cÃlculo das taxas originais, efetuamos o processo de suavizaÃÃo por mÃdias mÃveis, visando corrigir as flutuaÃÃes indesejadas obtidas na curva bruta de sobrevivÃncia. Mesmo apÃs o processo de suavizaÃÃo, optamos por restringir o estudo Ãs idades dentro do intervalo de 25 a 85 anos, dado o baixo nÃmero de Ãbitos e expostos nas idades supramencionadas. A partir da curva suavizada, aplicamos os modelos paramÃtricos de sobrevivÃncia de Gompertz, Gompertz-Makeham, Thiele e Helingman-Pollard, para testar o melhor ajuste da equaÃÃo. Os resultados mostraram que nenhum dos modelos paramÃtricos analisados se mostrou com robustez estatÃstica suficiente para se proceder a uma anÃlise preditiva com confiabilidade aceitÃvel. / This paper aims to calculate the survival rates of the participants of the Pension Funds electricity sector as well as finding the parametric survival model that best represents the data in the study. For development work we used data from 14 organizations with information of participants and retirees, with the exception of the disabled, for the period 2001 to 2009, amounting to a total of 100,000 lives analyzed. To calculate the crude rates of survival using the indirect method described in Ferreira (1985). After calculation of the original rates, we make the process of smoothing by moving averages in order to correct the unwanted fluctuations in the curve obtained crude survival. Even after the smoothing process, we chose to restrict the study to age within the range of 25 to 85 years, given the low number of deaths at ages above and exposed. From the smooth curve we apply the parametric models of survival Gompertz, Gompertz-Makeham, Thiele and Helingman-Pollard, to test the best fit of the equation. The results showed that none of the models proved to be analyzed with parametric statistical robust enough to conduct a predictive analysis with acceptable reliability.

Penalized methods are becoming more and more popular in statistical research. This dissertation research covers two major aspects of applications of penalized methods: variable selection and nonparametric function estimation. The following two paragraphs give brief introductions to each of the two topics. Infinite variance autoregressive models are important for modeling heavy-tailed time series. We use a penalty method to conduct model selection for autoregressive models with innovations in the domain of attraction of a stable law indexed by alpha is an element of (0, 2). We show that by combining the least absolute deviation loss function and the adaptive lasso penalty, we can consistently identify the true model. At the same time, the resulting coefficient estimator converges at a rate of n^(?1/alpha) . The proposed approach gives a unified variable selection procedure for both the finite and infinite variance autoregressive models. While automatic smoothing parameter selection for nonparametric function estimation has been extensively researched for independent data, it is much less so for clustered and longitudinal data. Although leave-subject-out cross-validation (CV) has been widely used, its theoretical property is unknown and its minimization is computationally expensive, especially when there are multiple smoothing parameters. By focusing on penalized modeling methods, we show that leave-subject-out CV is optimal in that its minimization is asymptotically equivalent to the minimization of the true loss function. We develop an efficient Newton-type algorithm to compute the smoothing parameters that minimize the CV criterion. Furthermore, we derive one simplification of the leave-subject-out CV, which leads to a more efficient algorithm for selecting the smoothing parameters. We show that the simplified version of CV criteria is asymptotically equivalent to the unsimplified one and thus enjoys the same optimality property. This CV criterion also provides a completely data driven approach to select working covariance structure using generalized estimating equations in longitudinal data analysis. Our results are applicable to additive, linear varying-coefficient, nonlinear models with data from exponential families.