Extending the Scope of Empirical Likelihood

By Nils Lid Hjort, Ian W. McKeague, I. Van Keilegom. 2009

243 citations recorded by the source corpus.

This article extends the scope of empirical likelihood methodology ill three directions: to allow for plug-in estimates Of nuisance parameters in estimating equations, slower than root n-rates of convergence, and settings in which there are a relatively large number of estimating equations compared to the sample size. Calibrating empirical likelihood confidence regions with plug-in is sometimes intractable due to the complexity of the asymptotics, so we introduce a bootstrap approximation that call be used in such situations. We provide a range of examples from survival analysis and nonparametric statistics to illustrate the main results.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ba522a1e9c604161b7016f5a3620546399b827fd

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Citations in the corpus

Penalized empirical likelihood and growing dimensional general estimating equations (2012, background): “In high dimensional empirical likelihood, the magnitude of||λθ|| is no longerOp(n−1/2) as in the fixed dimensional case (Hjort et al., 2009; Chen et al., 2009).”
Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random (2009, background): “In addition, we need to point out that theorem 2.1 in Hjort et al. (2009) cannot be applied directly in practice although they have provided a general framework for the ratio based on plug-in estimation, because their theorem does not answer how to construct an auxiliary random vector for a special…”
Empirical Likelihood for Non‐Smooth Criterion Functions (2009, background): “This idea has been considered in Hjort, McKeague and Van Keilegom (2008) in a general”
Empirical likelihood confidence intervals for nonparametric functional data analysis (2009, methodology): “(a) The general approach to show the convergence in distribution of the empirical likelihood ratio is laid out in Hjort et al. (2009). In particular, we only need to verify their assumptions (A1)-(A3), while assumption (A0) in their paper is directly assumed in (c0).”
Divergences and Duality for Estimation and Test under Moment Condition Models (2010, methodology): “Moreover, Hjort et al. (2009) extend the EL approach, to more general moment condition models, allowing the number of constraints to increase with growing sample size.”
Empirical likelihood confidence regions in a partially linear single‐index model (2006, unknown): “Recently, Hjort et al. (2004) have provided a general investigation on the ratio based on plug-in estimation.”
An updated review of Goodness-of-Fit tests for regression models (2013, methodology): “See the works by Hjort et al. (2009) and Van Keilegom et al.”
Robust Wasserstein profile inference and applications to machine learning (2016, background): “In the last three decades, there have been a great deal of successful applications of Empirical Likelihood for inference [33, 55, 11, 22, 36].”
Multivariate sign-based high-dimensional tests for sphericity (2014, background): “This challenge calls for new research on properties of traditional methods, see Chen et al. (2009) and Hjort et al. (2009), for instance, and new statistical approaches to deal with highdimensional data.”
High dimensional generalized empirical likelihood for moment restrictions with dependent data (2013, unknown): “Singleton (1982) for the GMM, Owen (1988), Qin and Lawless (1994) and Kitamura (1997) for the empirical likelihood (EL), Smith (1997), Newey and Smith (2004) and Anatolyev (2005) for the generalized empirical likelihood (GEL).”
A review on empirical likelihood methods for regression (2009, methodology): “The above asymptotic results can also be obtained from Hjort, McKeague and Van Keilegom (2009) , who developed generic conditions for the asymptotic theory of any EL ratio, built up using estimating equations depending on plug-in estimators of unknown nuisance parameters (see also Section 6.3).”
EMPIRICAL LIKELIHOOD FOR ESTIMATING EQUATIONS WITH MISSING VALUES (2009, methodology): “This phenomenon also appears when a nuisance parameter is replaced by a plugged-in estimator as revealed by Hjort, McKeague and Van Keilegom [13].”