el.test.wt {emplik}R Documentation

Weighted Empirical Likelihood ratio for mean, uncensored data

Description

This program is similar to el.test( ) except it takes weights, and is for one dimensional mu.

The mean constraint considered is:

sum_{i=1}^n p_i x_i = μ .

where p_i = Delta F(x_i) is a probability. Plus the probability constraint: sum p_i =1.

The weighted log empirical likelihood been maximized is

sum_{i=1}^n w_i log p_i.

Usage

el.test.wt(x, wt, mu)

Arguments

x a vector containing the observations.
wt a vector containing the weights.
mu a real number used in the constraint, weighted mean value of f(X).

Details

This function used to be an internal function. It becomes external because others may find it useful elsewhere.

The constant mu must be inside ( min x_i , max x_i ) for the computation to continue.

Value

A list with the following components:

x the observations.
wt the vector of weights.
prob The probabilities that maximized the weighted empirical likelihood under mean constraint.

Author(s)

Mai Zhou

References

Zhou, M. (2002). Computing censored empirical likelihood ratio by EM algorithm. Tech Report, Univ. of Kentucky, Dept of Statistics

Examples

## 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.EM(x,d,mu=3.5)
## we should get "-2LLR" = 1.2466....
myfun5 <- function(x, theta, eps) {
u <- (x-theta)*sqrt(5)/eps 
INDE <- (u < sqrt(5)) & (u > -sqrt(5)) 
u[u >= sqrt(5)] <- 0 
u[u <= -sqrt(5)] <- 1 
y <- 0.5 - (u - (u)^3/15)*3/(4*sqrt(5)) 
u[ INDE ] <- y[ INDE ] 
return(u)
}
el.cen.EM(x, d, fun=myfun5, mu=0.5, theta=3.5, eps=0.1)

[Package emplik version 0.9-5 Index]