el.CS.mean: Current Status Data Empirical Likellihood Test for the...

In emplikCS: Empirical Likelihood with Current Status Data for Mean, Probability, Hazard

Current Status Data Empirical Likellihood Test for the Parameter of Mean: mu(F)

Description

Given n current status data, we may estimate the CDF F(t) by NPMLE (e.g. by the isotNEW2() function in this package). Based on the NPMLE \hat F_n(t) we can estimate the mean mu(F).

This function, el.CS.mean, uses empirical likelihood to test the hypothesis that mu(F) equal to a given value(mu): i.e. H0: mu(F) = mu.

Empirical likelihood ratio test returns the Wilks statistics, -2LLR. The -2 log likelihood ratio under H0 is asymptotically chi square DF=1 distributed. See reference below.

Usage

 
el.CS.mean(mu, Itime, delta, Pfun) 

Arguments

mu	The hypothesized mean value.
Itime	The inspection times, a vector of length n.
delta	Either 0 or 1. I[yi <= ti]. length n.
Pfun	A given function, \Psi(s), used to define the (weighted) mean.

Details

This function tests the null hypothesis that mu(F) = mu versus not equal. We assume the data given is current status censored data.

The definition of the mean, mu(F) is

\mu(F) = \int_0^M [1- F(t)] d \Psi(t)

and its estimator based on (\delta_i, t_i) or \hat F_n is (assume \min(t_i) =0 or t_{(1)} =0)

{\mu(\hat F_n )} = \sum_{i=1}^n [1-\hat F_n(t_{(i)})] \Delta \Psi(t_{(i)})~,

where \Psi (t) is a given function and \Delta \Psi(t_{(i)})= \Psi (t_{(i+1)}) - \Psi(t_{(i)}) . If \Psi(t) =t in the above, then this is the ordinary mean (assuming F(t) has support (0, M) ).

The NPMLE \hat F_n(t) is convergent at cubic root n speed, but the mean estimator is convergent at ordinary root n speed. The -2LLR has chi square DF=1 null distribution asymptotically.

It goes without saying that we assume the NPMLE mu(hat F) has finite asymptotic variance (when normalized by root n).

Value

It returns a list containing

"-2LLR"

The Wilks statistics of the EL test, has approximate chi SQ DF=1 distribution under null hypothesis.

Author(s)

Mai Zhou <[e-mail]>.

References

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Huang, J. and Wellner, J. (1995). Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1 Statistica Neerlandica 49, 2, 153–163.

Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data Springer, New York.

Examples

N <- 300
set.seed(12345)
itime <- sort(c(rexp(N-1), 0.5) )       #### inspection times      
Stime <- rexp(N)                       #### survival times
delta <- as.numeric(Stime <= itime)    ####  current status censoring

emplikCS documentation built on June 21, 2026, 1:07 a.m.