Ημιπαραμετρική συμπερασματολογία για μοντέλα επιταχυνόμενων χρόνων ζωής
Semiparametric inference for accelerated life test models
KeywordsAccelerated life test models ; Density ratio models ; Distribution (Probability theory) ; Statistical analysis ; Bootstrap (Statistics)
Accelerated life time models are used in order to faster estimate life distributions of systems without waiting to observe their lifetimes under normal operating conditions. These models appeared many decades ago and are applied mainly in the areas of biostatistics and mechanical engineering. The purpose of this dissertation is to introduce the reader to this kind of models and to apply a semiparametric method of estimating the life time distribution. In the first chapter we start with a description of accelerated life test models by commenting on their usefulness and we continue with basic definitions of notions which are used in the dissertation. In the second chapter we present the density ratio model introduced by Fokianos et al. (2001) based on ideas of Qin and Lawless (1994) and we explain in detail the estimation process of its parameters via profiling the (nonparametric) likelihood. Based on the estimates of the parameters we estimate the unknown distribution function. The method is applied to a real data example. In the third chapter we discuss the density ratio model by further modeling its parameters. The simpler model is compared to the basic one asymptotically and using the bootstrap method. In the fourth chapter we consider the density ratio model in the case where the data are subject to (possible) random censoring. In this case our estimation procedures are based on a particular EM algorithm recently proposed by Wei and Zhou (2016). For the estimation of the models and all other calculations we used R and more specifically the function optim. The procedures which return the loglikelihood and its derivatives are presented in the fourth chapter. We conclude by discussing some questions and thoughts as well some ideas for future work.