Assessing the Effect of Individual Data Points on Inference from Empirical Likelihood

An oft-cited advantage of empirical likelihood is that the confidence intervals that are produced by this non-parametric technique are not necessarily symmetric. Rather, they reflect the nature of the underlying data and hence give a more representative way of reaching inferences about the functional of interest. However, this advantage can easily become a disadvantage if the resultant intervals are unduly influenced by some of the data points. In this paper, we consider the effect of extreme points, not necessarily outliers, on the profile empirical likelihood ratio and on empirical likelihood confidence intervals. In addition to suggesting diagnostics for detecting important observations, we examine the use of bootstrap and of jackknife influence functions to assess the extremity of suspect points.