EL-class {melt} | R Documentation |
EL class
Description
S4 class for empirical likelihood.
Details
Let be independent and identically distributed
-dimensional random variable from an unknown distribution
for
. We assume that
has a positive definite
covariance matrix. For a parameter of interest
, consider a
-dimensional smooth
estimating function
with a moment condition
We assume that there exists an unique that solves the above
equation. Given a value of
, the (profile) empirical likelihood
ratio is defined by
The Lagrange multiplier of the dual
problem leads to
where solves
Then the empirical log-likelihood ratio is given by
This problem can be efficiently solved by the Newton-Raphson method when
the zero vector is contained in the interior of the convex hull of
.
It is known that converges in
distribution to
, where
has a chi-square
distribution with
degrees of freedom. See the references below for
more details.
Slots
optim
A list of the following optimization results:
-
par
A numeric vector of the specified parameters. -
lambda
A numeric vector of the Lagrange multipliers of the dual problem corresponding topar
. -
iterations
A single integer for the number of iterations performed. -
convergence
A single logical for the convergence status. -
cstr
A single logical for whether constrained EL optimization is performed or not.
-
logp
A numeric vector of the log probabilities of the empirical likelihood.
logl
A single numeric of the empirical log-likelihood.
loglr
A single numeric of the empirical log-likelihood ratio.
statistic
A single numeric of minus twice the empirical log-likelihood ratio with an asymptotic chi-square distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the
-value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weights
A numeric vector of the re-scaled weights used for the model fitting.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
data
A numeric matrix of the data for the model fitting.
control
An object of class ControlEL constructed by
el_control()
.
References
Owen A (2001). Empirical Likelihood. Chapman & Hall/CRC. doi:10.1201/9781420036152.
Qin J, Lawless J (1994). “Empirical Likelihood and General Estimating Equations.” The Annals of Statistics, 22(1), 300–325. doi:10.1214/aos/1176325370.
Examples
showClass("EL")