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Parameters defined via general estimating equations (GEE) can be estimated bymaximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72(2004) 219--255] have recently shown that this EL estimator exhibits desirablehigher-order asymptotic properties, namely, that its $O(n^{-1})$ bias is smalland that bias-corrected EL is higher-order efficient. Although EL possessesthese properties when the model is correctly specified, this paper shows that,in the presence of model misspecification, EL may cease to be root n convergentwhen the functions defining the moment conditions are unbounded (even whentheir expectations are bounded). In contrast, the related exponential tilting(ET) estimator avoids this problem. This paper shows that the ET and ELestimators can be naturally combined to yield an estimator called exponentiallytilted empirical likelihood (ETEL) exhibiting the same $O(n^{-1})$ bias and thesame $O(n^{-2})$ variance as EL, while maintaining root n convergence undermodel misspecification.

Point estimation with exponentially tilted empirical likelihood