Maximum smoothed likelihood estimators for the interval censoring model
The Annals of Statistics · 2014 · Volume 42 · Issue 5
Abstract
We study the maximum smoothed likelihood estimator (MSLE) for interval censoring, case 2, in the so-called separated case. Characterizations in terms of convex duality conditions are given and strong consistency is proved. Moreover, we show that, under smoothness conditions on the underlying distributions and using the usual bandwidth choice in density estimation, the local convergence rate is $n^{-2/5}$ and the limit distribution is normal, in contrast with the rate $n^{-1/3}$ of the ordinary maximum likelihood estimator.
Keywords
62G05, 62G20, 62N01, asymptotic distribution, consistency, integral equations, interval censoring, kernel estimators, maximum smoothed likelihood estimator, smoothed maximum likelihood estimator
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