Abstract
The NPMLE in the bivariate censoring model is not consistent. The problem is caused by the singly censored observations. In this paper we prove that the NPMLE based on interval censoring the singly censored observations is ecient for this reduced data and moreover if we let the width of the interval converge to zero slowly enough, then the NPMLE is also ecient for the original data. We are able to determine a lower bound for the rate at which the bandwidth should converge to zero. The eciency proof uses the general identity which holds for NPMLE of a linear parameter in convex models as proved in van der Laan (1993a).
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