Empirical likelihood as a goodness-of-fit measure

The method of empirical likelihood can be viewed as one of allocating probabilities to an n-cell contingency table so as to minimise a goodness-of-fit criterion. It is shown that, when the Cressie-Read power-divergence statistic is used as the criterion, confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the Cressie-Read parameter lambda, including - 1, maximum entropy, 0, empirical likelihood, and I, Pearson's chi(2). It is noted that, in the power-divergence family, empirical likelihood is the only member which is Bartlett-correctable. However, simulation results suggest that, for the mean, using a scaled F distribution yields more accurate coverage levels for moderate sample sizes.