Empirical Cressie-read Discrepancy Statistics with Moment Restrictions

Abstract: This paper investigates the family of empirical Cressie-Read discrepancy statistics with moment restric-tions, which is a generalization of Baggerly(1998). It is shown that the statistics in the family are all st-order equivalent to empirical likelihood under suitable conditions, and hence, they are all asymptotically 2 distributed and the corresponding estimators of the parameters are all asymptotically normal. The rst-order eciency, using conventional Pitman approach based on the comparison of local power, of these statistics is veried. Furthermore, It is proved that the empirical likelihood ratio is the unique member of the family to be locally unbiased, which is consistent with the results of Bravo (2003). References [1] Baggerly, K. (1998). Empirical Likelihood as a Goodness of Fit Measure, Biometrika, 85, 535-547