  Empirical likelihood is a popular nonparametric or semi-parametric
statistical method with many nice statistical properties. Yet when the sample
size is small, or the dimension of the accompanying estimating function is
high, the application of the empirical likelihood method can be hindered by low
precision of the chi-square approximation and by nonexistence of solutions to
the estimating equations. In this paper, we show that the adjusted empirical
likelihood is effective at addressing both problems. With a specific level of
adjustment, the adjusted empirical likelihood achieves the high-order precision
of the Bartlett correction, in addition to the advantage of a guaranteed
solution to the estimating equations. Simulation results indicate that the
confidence regions constructed by the adjusted empirical likelihood have
coverage probabilities comparable to or substantially more accurate than the
original empirical likelihood enhanced by the Bartlett correction.
