Accompanying document to "Point Estimation with Exponentially Tilted Empirical Likelihood"

By Susanne M. Schennach. 2005

208 citations recorded by the source corpus.

Parameters defined via General Estimating Equations (GEE) can be estimated by maximizing the Empirical Likelihood (EL). Newey and Smith (2004) 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.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f91b280f215b93209fc4ccc0c43dac8aaa622e9c

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In Economics and Econometrics

1. Xuming He
2. Ivan Mizera
3. Sheung Chi Phillip Yam
4. Jiahua Chen
5. Yunwen Yang
6. Zheng Zhang
7. Kwun Chuen Gary Chan
8. Yukun Liu

In Finance

1. Ivan Mizera
2. Sheung Chi Phillip Yam
3. Jiahua Chen
4. Yunwen Yang
5. Zheng Zhang
6. Kwun Chuen Gary Chan
7. Yukun Liu
8. Amor Keziou

In Statistics and Probability

1. Xuming He
2. Roger W. Koenker
3. Yunwen Yang
4. Michel Broniatowski
5. Shu Yang
6. Ivan Mizera
7. Sheung Chi Phillip Yam
8. Jiahua Chen

Citations in the corpus

• Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting (2015, methodology): “For balancing an overidentified system of equations by using the empirical likelihood, there is no guarantee that the γ-estimate is √ N consistent (Schennach, 2007) under a misspecified propensity score model.”
• Propensity Score Weighting for Causal Inference with Clustered Data (2017, methodology): “We use the Kullback–Leibler distance function, which leads to exponential tilting estimation [57, 58, 59].”
• GEL CRITERIA FOR MOMENT CONDITION MODELS (2011, unknown): “More recently, Schennach (2007) and Smith (2007) propose GEL-related estimators that share the higher-order properties of EL.”
• Divergences and Duality for Estimation and Test under Moment Condition Models (2010, background): “Schennach (2007) discussed the asymptotic properties of the empirical likelihood estimate under misspecification; She showed the important fact that the EL estimate may cease to be root n consistent when the functions defining the moments conditions are unbounded.”
• QUASI-CONCAVE DENSITY ESTIMATION (2010, background): “See, for example, Shennach (2007). One could continue in this fashion marching inexorably toward weaker and weaker concavity requirements.”
• ADJUSTED EMPIRICAL LIKELIHOOD WITH HIGH-ORDER PRECISION (2010, methodology): “In this subsection, we examine the AEL through an asset-pricing model investigated by Hall and Horowitz (1996) and also by Imbens, Spady and Johnson (1998) expanded with q (q ≥ 2) moment restrictions by Schennach (2007).”
• Bayesian empirical likelihood for quantile regression (2012, methodology): “The GMM estimators, the maximum empirical likelihood estimators (MELE) and some other EL-type estimators generally have the same asymptotic distributions, but possibly different higher order asymptotic properties; see Newey and Smith (2004) and Schennach (2007).”