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

2005/12/08 by Susanne M. Schennach, Schennach, Susanne M.
Economics, Econometrics and Finance · Mathematics · #62F10 #62F12 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Finance (q-fin.ST) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0512181

openalex publication_date 2005/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Parameters defined via General Estimating Equations (GEE) can be estimated by\nmaximizing the Empirical Likelihood (EL). Newey and Smith (2004) have recently\nshown that this EL estimator exhibits desirable higher-order asymptotic\nproperties, namely, that its O(n^-1) bias is small and that bias-corrected EL\nis higher-order efficient. Although EL possesses these properties when the\nmodel is correctly specified, this paper shows that, in the presence of model\nmisspecification, EL may cease to be root n convergent when the functions\ndefining the moment conditions are unbounded (even when their expectations are\nbounded). In contrast, the related Exponential Tilting (ET) estimator avoids\nthis problem. This paper shows that the ET and EL estimators can be naturally\ncombined to yield an estimator called Exponentially Tilted Empirical Likelihood\n(ETEL) exhibiting the same O(n^-1) bias and the same O(n^-2) variance as EL,\nwhile maintaining root n convergence under model misspecification.\n

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