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Biometrika. Mar 2010; 97(1): 79–93.
PMCID: PMC2841365
NIHMSID: NIHMS184159
Generalized empirical likelihood methods for analyzing longitudinal data
Suojin Wang
Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A., sjwang/at/stat.tamu.edu
Lianfen Qian
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431, U.S.A., lqian/at/fau.edu
Raymond J. Carroll
Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A., carroll/at/stat.tamu.edu
Received April 2008; Revised June 2009
Efficient estimation of parameters is a major objective in analyzing longitudinal data. We propose two generalized empirical likelihood-based methods that take into consideration within-subject correlations. A nonparametric version of the Wilks theorem for the limiting distributions of the empirical likelihood ratios is derived. It is shown that one of the proposed methods is locally efficient among a class of within-subject variance-covariance matrices. A simulation study is conducted to investigate the finite sample properties of the proposed methods and compares them with the block empirical likelihood method by You et al. (2006) and the normal approximation with a correctly estimated variance-covariance. The results suggest that the proposed methods are generally more efficient than existing methods that ignore the correlation structure, and are better in coverage compared to the normal approximation with correctly specified within-subject correlation. An application illustrating our methods and supporting the simulation study results is presented.
Some key words: Confidence region, Efficient estimation, Empirical likelihood, Longitudinal data, Maximum empirical likelihood estimator
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