el_eval | R Documentation |
Computes empirical likelihood with general estimating functions.
el_eval(g, weights = NULL, control = el_control())
g |
A numeric matrix, or an object that can be coerced to a numeric matrix. Each row corresponds to an observation of an estimating function. The number of rows must be greater than the number of columns. |
weights |
An optional numeric vector of weights to be used in the
fitting process. The length of the vector must be the same as the number of
rows in |
control |
An object of class ControlEL constructed by
|
Let X_i
be independent and identically distributed
p
-dimensional random variable from an unknown distribution P
for i = 1, \dots, n
. We assume that P
has a positive definite
covariance matrix. For a parameter of interest
\theta(F) \in {\rm{I\!R}}^p
, consider a p
-dimensional smooth
estimating function g(X_i, \theta)
with a moment condition
\textrm{E}[g(X_i, \theta)] = 0.
We assume that there exists an unique \theta_0
that solves the above
equation. Given a value of \theta
, the (profile) empirical likelihood
ratio is defined by
R(\theta) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i g(X_i, \theta) = 0, p_i \geq 0, \sum_{i = 1}^n p_i = 1
\right\}.
el_mean()
computes the empirical log-likelihood ratio statistic
-2\log R(\theta)
with the n
by p
numeric matrix g
,
whose i
th row is g(X_i, \theta)
. Since the estimating function
can be arbitrary, el_eval()
does not return an object of class
EL, and the associated generics and methods are not
applicable.
A list of the following optimization results:
optim
A list with the following optimization results:
lambda
A numeric vector of the Lagrange multipliers of the dual
problem.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
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 p
-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.
Qin J, Lawless J (1994). “Empirical Likelihood and General Estimating Equations.” The Annals of Statistics, 22(1), 300–325. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/aos/1176325370")}.
EL, el_control()
set.seed(123526)
mu <- 0
sigma <- 1
x <- rnorm(100)
g <- matrix(c(x - mu, (x - mu)^2 - sigma^2), ncol = 2)
el_eval(g, weights = rep(c(1, 2), each = 50))
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