| el.cen.test {emplik} | R Documentation |
This program computes the maximized (wrt w_i) empirical log likelihood function for right censored data with the MEAN constraint:
sum_i [ d_i w_i f(x_i) ] = int f(t) dF(t) = μ
where w_i = Delta F(x_i) is a probability,
d_i is the censoring indicator.
It then computes the -2 log
empirical likelihood ratio which should be chi-square
distributed if the constraint is true.
Here F(t) is the (unknown) CDF;
f(t) can be any given left
continuous function in t.
μ is a given constant.
The data must contain some right censored observations.
If there is no censoring or the only censoring is the largest
observation, the code will stop and we should use
el.test that is for uncensored data.
el.cen.test(x,d,fun=function(x){x},mu,error=1e-8,maxit=20)
x |
a vector containing the observed survival times. |
d |
a vector containing the censoring indicators, 1-uncensor; 0-censor. |
fun |
a left continuous (weight) function used to calculate
the mean H_0.
fun(t) must be able to take a vector input t.
Default to the identity function f(t)=t. |
mu |
a real number used in the constraint, sum to this value. |
error |
an optional positive real number specifying the tolerance of iteration error in the QP. This is the L_1 norm of the differnence of two successive weights. |
maxit |
an optional integer, used to control maximum number of iterations. |
This function, unlike other functions in this package, can be slow for larger sample sizes. It took about one minute for a sample of size 2000 with 20% censoring on a 1GHz, 256MB PC.
When the given constants μ is too far away from the NPMLE, there will be no distribution satisfy the constraint. In this case the computation will stop. The minus 2 Log empirical likelihood ratio should be infinite.
The constant mu must be inside
( min f(x_i) , max f(x_i) )
for the computation to continue.
It is always true that the NPMLE values are feasible. So when the
computation stops, try move the mu closer
to the NPMLE, or use a different fun.
A list with the following components:
"-2LLR" |
The -2Log Likelihood ratio. |
xtimes |
the location of the hazard jumps. |
weights |
the jump size of CDF function at those locations. |
Pval |
P-value |
error |
the L_1 norm between the last two wts. |
iteration |
number of iterations carried out |
Mai Zhou, Kun Chen
Chen and Zhou (2000). Computing censored empirical likelihood ratio using Quadratic Programming. Tech Report, Univ. of Kentucky, Dept of Statistics
el.cen.test(rexp(100), c(rep(0,25),rep(1,75)), mu=1.5) ## second example with tied observations x <- c(1, 1.5, 2, 3, 4, 5, 6, 5, 4, 1, 2, 4.5) d <- c(1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1) el.cen.test(x,d,mu=3.5) # we should get "-2LLR" = 1.246634 etc.