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 nonparametric 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 one of the data points. This article proposes simple methods for evaluating the effect of single points 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.