Empirical likelihood displacement

Computes empirical likelihood displacement for model diagnostics and outlier detection.

Usage

# S4 method for EL
eld(object, control = NULL)

# S4 method for GLM
eld(object, control = NULL)

Arguments

object

An object that inherits from EL.

control

An object of class ControlEL constructed by el_control(). Defaults to NULL and inherits the control slot in object.

Value

An object of class ELD.

Details

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 \(i = 1, \dots, n \).

References

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. 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. doi:10.1093/biomet/asm094 .

See also

EL, ELD, el_control(), plot()

Examples

data("precip")
fit <- el_mean(precip, par = 30)
eld <- eld(fit)
plot(eld)