Asymptotic results on a general classof empirical statistics: power and confidenceinterval properties

摘要

We consider a very general class of empirical statistics that includes (a)empirical discrepancy (ED) statistics, (b) generalized empirical exponential familylikelihood statistics, (c) generalized empirical likelihood statistics, (d) empiricalstatistics arising from Bayesian considerations, and (e) Bartlett-type adjusted versionsof ED statistics. With reference to this general class, we investigate higherorder asymptotics on power and expected lengths of confidence intervals. For (b)-(e), such results have been hitherto unexplored. Furthermore, our findings helpin understanding the presently known results on the subclass (a) from a widerperspective.