Weighted Empirical Likelihood ratio for mean, uncensored data
This program is similar to el.test( ) except
it takes weights, and is for one dimensional mu.
The mean constraint considered is:
∑_{i=1}^n p_i x_i = μ .
where p_i = Δ F(x_i) is a probability. Plus the probability constraint: ∑ p_i =1.
The weighted log empirical likelihood been maximized is
∑_{i=1}^n w_i \log p_i.
el.test.wt(x, wt, mu, usingC=TRUE)
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). |
usingC |
TRUE: use C function, which may be benifit when sample size is large; FALSE: use pure R function. |
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.
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. |
Mai Zhou, Y.F. Yang for C part.
Owen, A. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18, 90-120.
Zhou, M. (2002). Computing censored empirical likelihood ratio by EM algorithm. Tech Report, Univ. of Kentucky, Dept of Statistics
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.