Estimation of a monotone density based on interval censored
observations

Geurt Jongbloed (VU Amsterdam)

Joint work with Lutz D\"umbgen (Bern) and Sandra Freitag (Kiel) 


From various perspectives, the problems of estimating a decreasing density
from direct observations and of estimating a distribution function from
current status data are related. The maximum likelihood estimators in both 
problems have $n^{-1/3}$ (pointwise) asymptotics and both estimators
are solutions to standard isotonic regression problems. Consequently, the
estimators can be computed using tools from the theory of isotonic regression.


In this talk we consider maximum likelihood estimation in problem that is
a combination of the two described above. Estimating a monotone density 
based on interval censored observations. Computational and asymptotic
issues of the maximum likelihood estimator will be addressed. 


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{\bf References}\\
Duembgen, L., Freitag, S.\ and Jongbloed, G.\ (2002a) Consistency
in concave regression with an application to current status data. Manuscript
in progress.\\


\noindent
Duembgen, L., Freitag, S.\ and Jongbloed, G.\ (2002b) Estimating a unimodal
distribution from interval censored data. Manuscript in progress.\\


\noindent
Huang, Y.\ and Zhang, C.-H.\ (1994). Estimating a monotone 
density from censored observations. {\it Ann. Statist.} {\bf 22}, 1256--1274