Empirical likelihood confidence intervals for M-functionals in the presence of auxiliary information

In this paper, we employ the method of empirical likelihood to construct confidence intervals for M-functionals in the presence of auxiliary information under a nonparametric setting. The modified empirical likelihood confidence intervals which make use of the knowledge of auxiliary information are asymptotically at least as narrow as the standard ones which do not utilize auxiliary information. For testing a hypothesis about a M-functional, the power of a test statistic based on the modified empirical likelihood ratio is larger than the one based on the standard empirical likelihood ratio. A simulation study is presented to demonstrate the performance of the modified empirical likelihood confidence intervals for small samples.