el.trun.test | R Documentation |
This program uses EM algorithm to compute the maximized
(wrt p_i
) empirical
log likelihood function for left truncated data with
the MEAN constraint:
\sum p_i f(x_i) = \int f(t) dF(t) = \mu ~.
Where p_i = \Delta F(x_i)
is a probability.
\mu
is a given constant.
It also returns those p_i
and the p_i
without
constraint, the Lynden-Bell estimator.
The log likelihood been maximized is
\sum_{i=1}^n \log \frac{\Delta F(x_i)}{1-F(y_i)} .
el.trun.test(y,x,fun=function(t){t},mu,maxit=20,error=1e-9)
y |
a vector containing the left truncation times. |
x |
a vector containing the survival times. truncation means x>y. |
fun |
a continuous (weight) function used to calculate
the mean as in |
mu |
a real number used in the constraint, mean value of |
error |
an optional positive real number specifying the tolerance of
iteration error. This is the bound of the
|
maxit |
an optional integer, used to control maximum number of iterations. |
This implementation is all in R and have several for-loops in it. A faster version would use C to do the for-loop part. But it seems faster enough and is easier to port to Splus.
When the given constants \mu
is too far
away from the NPMLE, there will be no distribution
satisfy the constraint.
In this case the computation will stop.
The -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 —
\sum_{d_i=1} p_i^0 f(x_i)
p_i^0
taken to be the jumps of the NPMLE of CDF.
Or use a different fun
.
A list with the following components:
"-2LLR" |
the maximized empirical log likelihood ratio under the constraint. |
NPMLE |
jumps of NPMLE of CDF at ordered x. |
NPMLEmu |
same jumps but for constrained NPMLE. |
Mai Zhou
Zhou, M. (2005). Empirical likelihood ratio with arbitrary censored/truncated data by EM algorithm. Journal of Computational and Graphical Statistics, 14, 643-656.
Li, G. (1995). Nonparametric likelihood ratio estimation of probabilities for truncated data. JASA 90, 997-1003.
Turnbull (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. JRSS B 38, 290-295.
## example with tied observations
vet <- c(30, 384, 4, 54, 13, 123, 97, 153, 59, 117, 16, 151, 22, 56, 21, 18,
139, 20, 31, 52, 287, 18, 51, 122, 27, 54, 7, 63, 392, 10)
vetstart <- c(0,60,0,0,0,33,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
el.trun.test(vetstart, vet, mu=80, maxit=15)
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