el_sd | R Documentation |
Computes empirical likelihood for the standard deviation.
el_sd(x, mean, sd, weights = NULL, control = el_control())
x |
A numeric vector, or an object that can be coerced to a numeric vector. |
mean |
A single numeric for the (known) mean value. |
sd |
A positive single numeric for the parameter value to be tested. |
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 length of
|
control |
An object of class ControlEL constructed by
|
Let X_i
be independent and identically random variable from an
unknown distribution P
for i = 1, \dots, n
. We assume that
{\textrm{E}[X_i]} = {\mu_0}
is known and that P
has a variance
\sigma_0^2
. Given a value of \sigma
, the
(profile) empirical likelihood ratio is defined by
R(\sigma) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i (X_i - \mu_0)^2 = \sigma^2,\
p_i \geq 0,\
\sum_{i = 1}^n p_i = 1
\right\}.
el_sd()
computes the empirical log-likelihood ratio statistic
-2\log R(\sigma)
, along with other values in SD.
An object of class SD.
EL, SD, el_mean()
, elt()
,
el_control()
data("women")
x <- women$height
w <- women$weight
fit <- el_sd(x, mean = 65, sd = 5, weights = w)
fit
summary(fit)
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