https://github.com/cran/emplik
Tip revision: f54d5e65d30ecadda3d5b4dd691f9c6f1b85d467 authored by Mai Zhou on 02 May 2012, 00:00:00 UTC
version 0.9-8-2
version 0.9-8-2
Tip revision: f54d5e6
el.test.wt2.Rd
\name{el.test.wt2}
\alias{el.test.wt2}
\title{Weighted Empirical Likelihood ratio for mean(s), uncensored data}
\usage{
el.test.wt2(x, wt, mu, maxit = 25, gradtol = 1e-07, Hessian = FALSE,
svdtol = 1e-09, itertrace = FALSE)
}
\description{
This program is similar to \code{el.test( )} except it takes weights.
The mean constraints are:
\deqn{ \sum_{i=1}^n p_i x_i = \mu . }
Where \eqn{p_i = \Delta F(x_i)} is a probability.
Plus the probability constraint: \eqn{ \sum p_i =1}.
The weighted log empirical likelihood been maximized is
\deqn{ \sum_{i=1}^n w_i \log p_i. }
}
\arguments{
\item{x}{a matrix (of size nxp) or vector containing the observations.}
\item{wt}{a vector of length n, containing the weights. If weights are
all 1, this is very simila to el.test. }
\item{mu}{a vector of length p, used in the constraint. weighted
mean value of \eqn{f(X)}.}
\item{maxit}{the maximum number of iteration.}
\item{gradtol}{the tolerance for a solution}
\item{Hessian}{if the Hessian needs to be computed?}
\item{svdtol}{ tolerance in perform SVD of the Hessian matrix. }
\item{itertrace}{TRUE/FALSE, if the intermediate steps needs to be printed.}
}
\value{
A list with the following components:
\item{lambda}{the Lagrange multiplier. Solution.}
\item{wt}{the vector of weights.}
\item{grad}{The gradian at the final solution.}
\item{nits}{number of iterations performed. }
\item{prob}{The probabilities that maximized the weighted
empirical likelihood under mean constraint.}
}
\details{
This function used to be an internal function.
It becomes external because others may find it useful.
It is similar to the function el.test( ) with the following
differences:
(1) The output lambda in el.test.wts, when divided by n
(the sample size or sum of all the weights) should be equal to the
output lambda in el.test.
(2) The Newton step of iteration in el.test.wts is different from
those in el.test. (even when all the weights are one).
}
\author{ Mai Zhou }
\references{
Zhou, M. (2002).
Computing censored empirical likelihood ratio
by EM algorithm.
\emph{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)
}
\keyword{nonparametric}
\keyword{htest}