Point estimation with exponentially tilted empirical likelihood

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.Comment: Published at http://dx.doi.org/10.1214/009053606000001208 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Bartlett correctability of empirical likelihood in generalized power divergence family

“…This result also implies that the exponentially tilted empirical likelihood statistic (i.e., the case of γ = −1 and φ = 0) considered by Schennach (2005Schennach ( , 2007 is not Bartlett correctable.…”

The Information Content of Implied Probabilities to Detect Structural Change

“…When we evaluate the weights at some estimators we obtain π ET t (θ T ) and π EL t (θ T ). Recently, Schennach (2004) combined ET and EL into the ETEL estimator that combines the advantages of each approach.…”

“…Bertille, Bonnal and Renault (2007) also related the informational content of the moment conditions to the weights and one of their contribution is in the use of the weights in a three step estimation procedure. Schennach (2004) also discusses the use of these weights in the context of model misspecification. Ramalho and Smith (2005) considered Pearson-type test statistics (statistics based on the difference between restricted and unrestricted estimators of the weights) for the validity of moment restrictions and parametric restrictions (see also Otsu (2006)).…”

Estimação de modelos DSGE usando verossimilhança empírica e mínimo contraste generalizados

“…Desta forma, o estimador GEL é expresso pelo problema de selâ SMITH, 2004;ANATOLYEV;GOSPODINOV, 2011). A escolha da função ρ(υ) define os seguintes estimadores: 1) verossimilhança empírica (EL) de Owen (1988), Qin e Lawless (1994) e Imbens (1997): ρ(υ) = ln(1 − υ); 2) exponential tilting (ET) de Kitamura e Stutzer (1997) e Imbens, Johnson e Spady (1998): ρ(υ) = exp(υ); 3) continuous updating (CUE) de Hansen, Heaton e Yaron (1996): , 2004;SCHENNACH, 2007;SMITH, 2011).…”

“…em que γ é um parâmetro de indexação, obtemos os estimadores da classe de estimadores GEL, que também pertencem a classe de estimadores GMC, atribuindo valores específicos para γ: CORCORAN, 1998;SMITH, 2004;SCHENNACH, 2007).…”