Journées de l'optimisation 2007 Optimizations days

The analysis of event history data deals with events and conditions that arise over the lifetime of individuals or systems in some population. It is a statistical topic applied in many branches of science such as actuarial science, biology, demography, economics, engineering, epidemiology, and medicine. In all these fields, considerable amount of information is often collected on the nature and timing of different events of interest. In this talk, I will first present this statistical topic and then discuss two research problems I am working on: inference methods when historical data are aggregated and bayesian approaches to predict future recurrent events.

We study the problem of variance estimation for a domain total when auxiliary value imputation, sometimes called cold-deck or substitution imputation, has been used to fill in missing data. We consider two approaches to inference, which lead to different variance estimators. In the first approach, the validity of an imputation model is required. Our proposed variance estimator is nevertheless robust to misspecification of the second moment of the model. Under this approach, we show the somewhat counter-intuitive result that the total variance of the imputed estimator can be smaller than the sampling variance of the complete-data estimator. We also show that the naïve variance estimator (i.e. the variance estimator obtained by treating the imputed values as observed values) is asymptotically a valid estimator of the total variance when the sampling fraction is negligible. In the second approach, the validity of an imputation model is not required but response probabilities need to be estimated. Our mean squared error estimator is obtained using robust estimates of response probabilities and is thus only weakly dependent on modeling assumptions. Finally, we propose an hybrid variance estimator which can be seen as a compromise between the two approaches. A simulation study illustrates the robustness of our proposed variance (mean squared error) estimators.

Dans cette conférence, nous proposons un modèle statistique bayésien empirique pour représenter le nombre d'accidents pour des flottes de camions au Québec de 1991 à 1998. La distribution des accidents dépendra de facteurs observables (caractéristiques de la flotte et des camions) considérés comme étant des hyperparamètres et d'effets aléatoires. Cette analyse des données de panel portera sur l'estimation des effets « firme » et « individuel ». Une approche bayésienne empirique sera utilisée pour estimer les différents hyperparamètres.