## The Annals of Statistics

### Point estimation with exponentially tilted empirical likelihood

Susanne M. Schennach

#### Abstract

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219–255] have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties, namely, that its O(n−1) bias is small and that bias-corrected EL is higher-order efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that, in the presence of model misspecification, EL may cease to be root n convergent when the functions defining the moment conditions are unbounded (even when their expectations are bounded). In contrast, the related exponential tilting (ET) estimator avoids this problem. This paper shows that the ET and EL estimators can be naturally combined to yield an estimator called exponentially tilted empirical likelihood (ETEL) exhibiting the same O(n−1) bias and the same O(n−2) variance as EL, while maintaining root n convergence under model misspecification.

#### Article information

Source
Ann. Statist., Volume 35, Number 2 (2007), 634-672.

Dates
First available in Project Euclid: 5 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1183667287

Digital Object Identifier
doi:10.1214/009053606000001208

Mathematical Reviews number (MathSciNet)
MR2336862

Zentralblatt MATH identifier
1117.62024

Subjects
Primary: 62F10: Point estimation
Secondary: 62F12: Asymptotic properties of estimators

#### Citation

Schennach, Susanne M. Point estimation with exponentially tilted empirical likelihood. Ann. Statist. 35 (2007), no. 2, 634--672. doi:10.1214/009053606000001208. https://projecteuclid.org/euclid.aos/1183667287

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