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Title: Non-existence, non-uniqueness and potential uselessness of the NPMLE for doubly truncated data Authors:  Carla Moreira - University of Minho (Portugal) [presenting]
Jacobo de Una-Alvarez - Universidade de Vigo (Spain)
Abstract: Doubly truncated data are found in astronomy, epidemiology and survival analysis literature. They arise when each observation is confined to an interval; that is, the variable of interest is observed only when it falls within two random limits. The existing literature contains many nonparametric methods for dealing with truncated data. The nonparametric maximum likelihood estimator (NPMLE) for doubly truncated data has been developed. This estimator was obtained earlier for singly truncated data. To compute the NPMLE of the cumulative distribution function, iterative algorithms have been proposed. When analysing a particular doubly truncated dataset, non-existence or non-uniqueness of the NPMLE may occur; the NPMLE may be useless even when the iterative algorithms reach the convergence due to its huge variance. We present and analyse the age at diagnosis of Acute Coronary Syndrome dataset, in which these features concerned to the NPMLE appear. We apply the sufficient and necessary conditions introduced previously to investigate the existence and uniqueness of the NPMLE. We present a simulation study to investigate the impact of the width of the observational window in the potential uselessness of the NPMLE.