el.test {emplik}R Documentation

Empirical likelihood ratio test for the means, uncensored data


Compute the empirical likelihood ratio with the mean vector fixed at mu.

The log empirical likelihood been maximized is

\sum_{i=1}^n \log \Delta F(x_i).


el.test(x, mu, lam, maxit=25, gradtol=1e-7, 
                 svdtol = 1e-9, itertrace=FALSE)



a matrix or vector containing the data, one row per observation.


a numeric vector (of length = ncol(x)) to be tested as the mean vector of x above, as H_0.


an optional vector of length = length(mu), the starting value of Lagrange multipliers, will use 0 if missing.


an optional integer to control iteration when solve constrained maximization.


an optional real value for convergence test.


an optional real value to detect singularity while solve equations.


a logical value. If the iteration history needs to be printed out.


If mu is in the interior of the convex hull of the observations x, then wts should sum to n. If mu is outside the convex hull then wts should sum to nearly zero, and -2LLR will be a large positive number. It should be infinity, but for inferential purposes a very large number is essentially equivalent. If mu is on the boundary of the convex hull then wts should sum to nearly k where k is the number of observations within that face of the convex hull which contains mu.

When mu is interior to the convex hull, it is typical for the algorithm to converge quadratically to the solution, perhaps after a few iterations of searching to get near the solution. When mu is outside or near the boundary of the convex hull, then the solution involves a lambda of infinite norm. The algorithm tends to nearly double lambda at each iteration and the gradient size then decreases roughly by half at each iteration.

The goal in writing the algorithm was to have it “fail gracefully" when mu is not inside the convex hull. The user can either leave -2LLR “large and positive" or can replace it by infinity when the weights do not sum to nearly n.


A list with the following components:


the -2 loglikelihood ratio; approximate chisq distribution under H_o.


the observed P-value by chi-square approximation.


the final value of Lagrange multiplier.


the gradient at the maximum.


the Hessian matrix.


weights on the observations


number of iteration performed


Original Splus code by Art Owen. Adapted to R by Mai Zhou.


Owen, A. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18, 90-120.


x <- matrix(c(rnorm(50,mean=1), rnorm(50,mean=2)), ncol=2,nrow=50)
el.test(x, mu=c(1,2))
## Suppose now we wish to test Ho: 2mu(1)-mu(2)=0, then
y <- 2*x[,1]-x[,2]
el.test(y, mu=0)
xx <- c(28,-44,29,30,26,27,22,23,33,16,24,29,24,40,21,31,34,-2,25,19)
el.test(xx, mu=15)  #### -2LLR = 1.805702

[Package emplik version 1.1-1 Index]