AISM 53, 498-516

© 2001 ISM

## Weighted empirical likelihood ratio confidence intervals for the mean
with censored data

### Jian-Jian Ren

Department of Mathematics, Tulane University,
New Orleans, LA70118, U.S.A.

(Received June 25, 1998; revised June 7, 1999)

Abstract.
We propose a procedure to construct the empirical
likelihood ratio
confidence interval for the mean using a resampling method. This approach
leads
to the definition of a likelihood function for censored
data, called *weighted empirical likelihood function*. With the
second order
expansion of the log likelihood ratio, a weighted empirical
likelihood ratio confidence interval for the mean is proposed and shown by
simulation studies to have comparable coverage accuracy to
alternative methods, including the nonparametric bootstrap-$t$. The
procedures
proposed here apply in a unified way to different types of
censored data, such as right censored data, doubly censored data and interval
censored data, and computationally more efficient than the
bootstrap-$t$ method. An example of a set of doubly censored breast cancer
data
is presented with the application of our methods.

Key words and phrases:
Bootstrap, doubly censored data, interval censored data, leveraged bootstrap, right
censored data.

**Source**
(TeX , DVI )