A Semi-Parametric Maximum Likelihood Approach To Linear
Regression With Right-Censored Data
Abstract
Consider regression model, X=a+b Z+e, where X may be right censored
and e is a white noise. The Buckley-James estimator (BJE) of b has been
considered superior over other estimators. We show that the BJE is
inconsistent if P(e>M)>0, where M is a constant such that X is always
right censored if e>M. Two real data sets show that it is often that
P(e>M)>0 and the BJE may not make sense. We propose a new estimator of b
which is a modification of semi-parametric MLE's (SMLE) of b.
It is consistent even if P(e>M)>0.
When P(M>e)=1, simulations suggest that it equals b for moderate
large sample size if e is discrete, and converges as fast as
the BJE if e is continuous.
Moreover, it can be obtained by
a non-iterative algorithm. We compare these estimators using the above two
data sets. The results indicate that our estimates are more reliable and
robust than the BJE. Extension to the interval-censored data is also
studied.
R E F R E S H M E N T S
4:00 To 4:25 PM
Kenneth W. Anderson
Memorial Reading Room
