Expected lengths of confidence intervals based on empirical discrepancy statistics

Abstract

We consider a very general class of empirical discrepancy statistics that includes the Cressie-Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order asymptotics for expected lengths of associated confidence intervals are investigated. An explicit formula is worked out and its use for comparative purposes is discussed. It is seen that the empirical likelihood ratio statistic, which enjoys interesting second-order power properties, loses much of its edge under the present criterion.