el.test.wt: Weighted Empirical Likelihood ratio for mean, uncensored data In emplik: Empirical Likelihood Ratio for Censored/Truncated Data

Description

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.

Usage

 `1` ```el.test.wt(x, wt, mu, usingC=TRUE) ```

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). `usingC` TRUE: use C function, which may be benifit when sample size is large; FALSE: use pure R function.

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, Y.F. Yang for C part.

References

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

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## 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) ```

emplik documentation built on May 29, 2017, 11:44 a.m.