Abstract
We consider the problem of estimating the distribution function, the density
and the hazard rate of the (unobservable) event time in the current status
model. A well studied and natural nonparametric estimator for the distribution
function in this model is the nonparametric maximum likelihood estimator
(MLE). We study two alternative methods for the estimation of the distribution
function, assuming some smoothness of the event time distribution.
The first estimator is based on a maximum smoothed likelihood approach.
The second method is based on smoothing the (discrete) MLE of the distribution
function. These estimators can be used to estimate the density and
hazard rate of the event time distribution based on the plug-in principle.
and the hazard rate of the (unobservable) event time in the current status
model. A well studied and natural nonparametric estimator for the distribution
function in this model is the nonparametric maximum likelihood estimator
(MLE). We study two alternative methods for the estimation of the distribution
function, assuming some smoothness of the event time distribution.
The first estimator is based on a maximum smoothed likelihood approach.
The second method is based on smoothing the (discrete) MLE of the distribution
function. These estimators can be used to estimate the density and
hazard rate of the event time distribution based on the plug-in principle.
| Original language | English |
|---|---|
| Pages (from-to) | 352-387 |
| Journal | Annals of Statistics |
| Volume | 38 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2010 |
| Externally published | Yes |
Keywords
- Current status data
- maximum smoothed likelihood
- smoothed maximum likelihood
- distribution estimation
- density estimation
- hazard rate estimation
- asymptotic distribution