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Generalized empirical likelihood methods for analyzing longitudinal data. (English) Zbl 1183.62060
Summary: 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 of J. You et al. [Can. J. Stat. 34, No. 1, 79–86 (2006 (2006; Zbl 1096.62033)] 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.
MSC:
62G05Nonparametric estimation
62G10Nonparametric hypothesis testing
62G08Nonparametric regression
62P10Applications of statistics to biology and medical sciences
65C60Computational problems in statistics