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We study the maximum smoothed likelihood estimator (MSLE) for intervalcensoring, case 2, in the so-called separated case. Characterizations in termsof convex duality conditions are given and strong consistency is proved.Moreover, we show that, under smoothness conditions on the underlyingdistributions and using the usual bandwidth choice in density estimation, thelocal convergence rate is $n^{-2/5}$ and the limit distribution is normal, incontrast with the rate $n^{-1/3}$ of the ordinary maximum likelihood estimator.

Maximum smoothed likelihood estimators for the interval censoring model