el.test.wt2 {emplik}R Documentation

Weighted Empirical Likelihood ratio for mean(s), uncensored data

Description

This program is similar to el.test( ) except it takes weights.

The mean constraints are:

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.wt2(x, wt, mu, maxit = 25, gradtol = 1e-07, Hessian = FALSE, 
    svdtol = 1e-09, itertrace = FALSE)

Arguments

x a matrix (of size nxp) or vector containing the observations.
wt a vector of length n, containing the weights.
mu a vector of length p, used in the constraint. weighted mean value of f(X).
maxit the maximum number of iteration.
gradtol the tol for a solution
Hessian if the Hessian needs to be computed?
svdtol tol in perform SVD of the matrix.
itertrace TRUE/FALSE, if the intermediate steps needs to be printed.

Details

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

Value

A list with the following components:

lambda the Lagrange multiplier.
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]