Computes empirical likelihood displacement for model diagnostics and outlier detection.
# S4 method for EL
eld(object, control = NULL)# S4 method for GLM
eld(object, control = NULL)
An object of class ELD.
An object that inherits from EL.
An object of class ControlEL constructed by
el_control(). Defaults to NULL and inherits the control slot in
object.
Let \(L(\theta)\) be the empirical log-likelihood function based
on the full sample with \(n\) observations. The maximum empirical
likelihood estimate is denoted by \(\hat{\theta}\). Consider a reduced
sample with the \(i\)th observation deleted and the corresponding
estimate \(\hat{\theta}_{(i)}\). The empirical likelihood displacement is
defined by
$$\textrm{ELD}_i = 2\{L(\hat{\theta}) - L(\hat{\theta}_{(i)})\}.$$
If \(\textrm{ELD}_i \) is large, then the \(i\)th observation is an
influential point and can be inspected as a possible outlier. eld
computes \(\textrm{ELD}_i \) for \(i = 1, \dots, n \).
Lazar NA (2005). ``Assessing the Effect of Individual Data Points on Inference From Empirical Likelihood.'' Journal of Computational and Graphical Statistics, 14(3), 626--642. tools:::Rd_expr_doi("10.1198/106186005X59568").
Zhu H, Ibrahim JG, Tang N, Zhang H (2008). ``Diagnostic Measures for Empirical Likelihood of General Estimating Equations.'' Biometrika, 95(2), 489--507. tools:::Rd_expr_doi("10.1093/biomet/asm094").
EL, ELD, el_control(), plot()
data("precip")
fit <- el_mean(precip, par = 30)
eld <- eld(fit)
plot(eld)
Run the code above in your browser using DataLab