Mathematical Sciences: Topics in Multivariate Survival Analysis and Counting Processes

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Three attacks on the problem of analysis of multivariate survival functions are to be made. First, notions of dependence and of asymmetry are to be incorporated into familiar formulations with product limit representations. Secondly, representations in terms of generalized cumulants of counting processes will be investigated. Third, estimators will be constructed for censored data from a Markov renewal process; and the prediction problem will be considered.