elt | R Documentation |
Tests a linear hypothesis with various calibration options.
## S4 method for signature 'EL'
elt(
object,
rhs = NULL,
lhs = NULL,
alpha = 0.05,
calibrate = "chisq",
control = NULL
)
object |
An object that inherits from EL. |
rhs |
A numeric vector or a column matrix for the right-hand side of
hypothesis, with as many entries as the rows in |
lhs |
A numeric matrix or a vector (treated as a row matrix) for the
left-hand side of a hypothesis. Each row gives a linear combination of the
parameters in |
alpha |
A single numeric for the significance level. Defaults to |
calibrate |
A single character representing the calibration method. It
is case-insensitive and must be one of |
control |
An object of class ControlEL constructed by
|
elt()
performs the constrained minimization of l(\theta)
described in CEL. rhs
and lhs
cannot be both NULL
. For
non-NULL
lhs
, it is required that lhs
have full row rank
q \leq p
and p
be equal to the number of parameters in the
object
.
Depending on the specification of rhs
and lhs
, we have the following
three cases:
If both rhs
and lhs
are non-NULL
, the constrained minimization
is performed with the right-hand side r
and the left-hand side
L
as
\inf_{\theta: L\theta = r} l(\theta).
If rhs
is NULL
, r
is set to the zero vector as
\inf_{\theta: L\theta = 0} l(\theta)
.
If lhs
is NULL
, L
is set to the identity matrix and the
problem reduces to evaluating at r
as l(r)
.
calibrate
specifies the calibration method used. Four methods are
available: "ael"
(adjusted empirical likelihood calibration), "boot"
(bootstrap calibration), "chisq"
(chi-square calibration), and "f"
(F
calibration). When lhs
is not NULL
, only "chisq"
is
available. "f"
is applicable only to the mean parameter. The an
slot in
control
applies specifically to "ael"
, while the nthreads
, seed
,
and B
slots apply to "boot"
.
An object of class of ELT. If lhs
is non-NULL
, the
optim
slot corresponds to that of CEL. Otherwise, it
corresponds to that of EL.
Adimari G, Guolo A (2010). “A Note on the Asymptotic Behaviour of Empirical Likelihood Statistics.” Statistical Methods & Applications, 19(4), 463–476. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10260-010-0137-9")}.
Chen J, Variyath AM, Abraham B (2008). “Adjusted Empirical Likelihood and Its Properties.” Journal of Computational and Graphical Statistics, 17(2), 426–443.
Kim E, MacEachern SN, Peruggia M (2024). “melt: Multiple Empirical Likelihood Tests in R.” Journal of Statistical Software, 108(5), 1–33. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v108.i05")}.
Qin J, Lawless J (1995). “Estimating Equations, Empirical Likelihood and Constraints on Parameters.” Canadian Journal of Statistics, 23(2), 145–159. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/3315441")}.
EL, ELT, elmt()
, el_control()
## Adjusted empirical likelihood calibration
data("precip")
fit <- el_mean(precip, 32)
elt(fit, rhs = 100, calibrate = "ael")
## Bootstrap calibration
elt(fit, rhs = 32, calibrate = "boot")
## F calibration
elt(fit, rhs = 32, calibrate = "f")
## Test of no treatment effect
data("clothianidin")
contrast <- matrix(c(
1, -1, 0, 0,
0, 1, -1, 0,
0, 0, 1, -1
), byrow = TRUE, nrow = 3)
fit2 <- el_lm(clo ~ -1 + trt, clothianidin)
elt(fit2, lhs = contrast)
## A symbolic description of the same hypothesis
elt(fit2, lhs = c(
"trtNaked - trtFungicide",
"trtFungicide - trtLow",
"trtLow - trtHigh"
))
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