On some inferential problems with recurrent event models
"Recurrent events (RE) occur in many disciplines, such as biomedical, engineering, actuarial science, sociology, economy to name a few. It is then important to develop dynamic models for their modeling and analysis. Of interest with data collected in a RE monitoring are inferential problems pertaining to the distribution function F of the time between occurrences, or that of the distribution function G of the monitoring window, and their functionals such as quantiles, mean. These problems include, but not limited to: estimating F parametrically or nonparametrically; goodness of fit tests on an hypothesized family of distributions; efficient of tests; regression-type models, or validation of models that arise in the modeling and analysis of RE. This dissertation work focuses on several inferential problems of significant importance with these types of data. The first one we dealt with is the problem of informative monitoring. Informative monitoring occurs when G contains information about F, and the information is accounted for in the inferential process through a Lehman-type model, 1 - G= (1 -F )ß, so called generalized Koziol-Green model in the literature. We propose a class of inferential procedures for validating the model. The research work proceeds with the development of a flexible, random cells based chi-square goodness of fit test for an hypothesized family of distributions with unknown parameter. The cells are random in the sense that they are cut free, are function of the data, and are not predetermined in advance as is done in standard chi-square type tests. A minimum chi-square estimator is used to construct the test statistic whose power is assessed against a sequence of Pitman-like alternatives. The last problem we considered is that of an efficiency, optimality, and comparison of various statistical tests on RE that are derived in this work and existed in the literature. The efficiency and optimality are obtained by extending the theory of Bahadur and Wieand to RE. Asymptotic properties of the different estimators and or statistics are presented via empirical processes tools. Small sample results using intensive simulation study of the various procedures are presented, and these show good approximation of the truth. Real recurrent event data from the engineering and biomedical studies are utilized to illustrate the various methods"--Abstract, page iv.
Missouri University of Science and Technology
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