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Abstract:
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In statistics one often has to find a method for analyzing data which are only indirectly given. One such situation is when one has ``current status data", which only give the information that a certain event has taken place or on the other hand still did not happen. So one observes the ``current status" of the matter. We consider a simple linear regression model where the dependent variable is not observed due to current status censoring and where no assumptions are made on the distribution of the unobserved random error terms. For this model, the theoretical performance of the maximum likelihood estimator (MLE), maximizing the likelihood of the data over all possible distribution functions and all possible regression parameters, is still an open problem. We construct estimators for the finite dimensional regression parameter using ``non smooth'' score equations that depend on the piecewise-constant MLE for the distribution function of the random error. The estimators are $\sqrt{n}$-consistent and asymptotically normally distributed. We illustrate the behavior of and compare our estimates with competitive estimates using simulations.
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