When there exist time-dependent covariates in some longitudinal study,it is well-known that the widely used generalized estimating equations approach would not preserve unbiasedness and robustness in an arbitrary working correlation structure.However,incorrect application of the working correlation structure could result in loss of efficiency and biased estimation.To deal with this problem,Leung et al.proposed a shrinkage empirical likelihood approach which combines the unbiased estimating equations and the extracted additional information from the estimating equations that excluded by the independence assumption.Although their simulations have shown the proposed estimators are efficient,the asymptotic properties of the proposed estimators are unknown.Here it is was shown that the proposed estimators are consistent and asymptotically normally distributed under some regular conditions.%在一些纵向研究中,协变量往往依赖于观测时间,此时流行的广义估计方程方法在任意的工作相关矩阵下不再保持估计的无偏性和稳健性,若仅使用独立工作相关矩阵则会造成效率低下,而使用不合适的工作相关矩阵可能会错误地包含有偏估计函数,最终导致估计有偏.为此,Leung等提出一种压缩的经验似然估计方法,将大量的无偏估计函数和其他辅助估计函数综合起来,模拟研究表明所提方法相比传统方法是有效的.但他们对其理论性质并未研究.这里对这种压缩经验似然估计量的大样本性质进行了研究,证明了在合适的条件下,压缩经验似然估计量具有相合性和渐近正态性,并给出了经验似然比的渐近分布.
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