Large dimensional empirical likelihood

The empirical likelihood is a versatile nonparametric approach to testing hypotheses and constructing confidence regions. However it is not clear if the famous Wilks’ theorem still works in high dimensions. In this paper, by adding two pseudo-observations to the original data set, we prove the asymptotic normality of the log empirical likelihood ratio statistic when the sample size and the data dimension are comparable. In practice, we suggest to use the normalized F (p;n − p) distribution to approximate its distribution. Simulation results show the excellent performance of this approximation.