Current Status Data in the Twenty-First Century: Some Interesting Developments - Interval-Censored-Time-to-Event Data: Methods and Applications - page 74

bias and variance can be explicitly computed. A comparison of this result
to the asymptotics for F M n shows that the asymptotic variance is the same
in both cases; however, the asymptotic biases are unequal and there is no

monotone ordering between the two. Thus, in some situations the MSLE may

work better than the SMLE, and vice versa. Groeneboom et al. (2010) dis-

cuss a bootstrapped-based method for bandwidth selection but do not provide

simulation-based evidence of the performance of their method. The work in

Groeneboom et al. (2010) raises an interesting question. Consider a practi-

tioner who wants to construct a confidence interval for F(t 0 ) in the current
status model and let us suppose that the practitioner is willing to assume that

F around t 0 is reasonably smooth (say, three times differentiable). She could
either use the likelihood ratio technique from Banerjee and Wellner (2005) or

the smoothed likelihood approach of Groeneboom et al. (2010). The former

technique would avoid bandwidth specification and also the estimation of nui-

sance parameters. The latter would need active bandwidth selection and also

nuisance parameter estimation. In this respect, the likelihood inversion pro-
cedure is methodologically cleaner. On the other hand, because the smoothed

estimators achieve a higher convergence rate (n 2=5 as opposed to n 1=3 obtained

through likelihood-based procedures), the CIs based on these estimators would

be asymptotically shorter than the ones based on likelihood ratio inversion. So,
there is a trade-off here. The n 1=15

faster rate of convergence of the smoothed

MLE will start to show at large sample sizes, but at smaller sample sizes,

bandwidth selection and the estimation of nuisance parameters from the data

would introduce much more variability in the intervals based on the smoothed

MLE. There is, therefore, a need for a relative study of these two procedures

in terms of actual performance at different sample sizes.

Groeneboom et al. (2011) also use kernel smoothed estimators to remedy

the inconsistency of the MLE in the continuous marks model under current

status censoring. They develop a version of the MSLE in this model following

similar ideas as in the above paper: the log-likelihood function for the observed