Empirical likelihood displacement

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)

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 .

Examples

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