Schennach (2007) has shown that the Empirical Likelihood (EL) estimator may not be asymptotically normal when a misspecified model is estimated. This problem occurs because the empirical probabilities of individual observations are restricted to be positive. I find that even the EL estimator computed without the restriction can fail to be asymptotically normal for misspecified models if the sample moments weighted by unrestricted empirical probabilities do not have finite population moments. As a remedy for this problem, I propose a group of alternative estimators which I refer to as modified EL (MEL) estimators. For correctly specified models, these estimators have the same higher order asymptotic properties as the EL estimator. The MEL estimators are obtained by the Generalized Method of Moments (GMM) applied to an exactly identified model. The simulation results provide promising evidence for these estimators. In the second chapter, I introduce an alternative group of estimators to the Generalized Empirical Likelihood (GEL) family. The new group is constructed by employing demeaned moment functions in the objective function while using the original moment functions in the constraints. This designation modifies the higher-order properties of estimators. I refer to these new estimators as Demeaned Generalized Empirical Likelihood (DGEL) estimators. Although Newey and Smith (2004) show that the EL estimator in the GEL family has fewer sources of bias and is higher-order efficient after bias-correction, the demeaned exponential tilting (DET) estimator in the DGEL group has those superior properties. In addition, if data are symmetrically distributed, every estimator in the DGEL family shares the same higher-order properties as the best member.