2010/03/08 by Yukun Liu, Jiahua Chen · 85 citations
Mathematics · #Advanced Statistical Methods and Models #Confidence interval #Econometrics #Empirical likelihood #Estimating equations #Estimator #Likelihood function #Likelihood principle #Likelihood-ratio test #Mathematics #Maximum likelihood #Nonparametric statistics #Parametric statistics #Quasi-maximum likelihood #Restricted maximum likelihood #Sample size determination #Small area estimation #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #math.ST #stat.TH
paper · pdf · doi:10.1214/09-aos750
published in The Annals of Statistics 38(3) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/09-AOS750 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2010/03/08 · arxiv created 2010/10/02 · arxiv updated 2010/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective at addressing both problems. With a specific level of adjustment, the adjusted empirical likelihood achieves the high-order precision of the Bartlett correction, in addition to the advantage of a guaranteed solution to the estimating equations. Simulation results indicate that the confidence regions constructed by the adjusted empirical likelihood have coverage probabilities comparable to or substantially more accurate than the original empirical likelihood enhanced by the Bartlett correction.