Abstract

The quadratic inference function approach is a popular method in the analysis of correlated data. The quadratic inference function is formulated based on multiple sets of score equations (or extended score equations) that over-identify the regression parameters of interest, and improves efficiency over the generalized estimating equations under correlation misspecification. In this note, we provide an alternative solution to the quadratic inference function by separately solving each set of score equations and combining the solutions. We provide an insight that an optimally weighted combination of estimators obtained separately from the distinct sets of score equations is asymptotically equivalent to the estimator obtained via the quadratic inference function. We further establish results on inference for the optimally weighted estimator and extend these insights to the general setting with over-identified estimating equations. A simulation study is carried out to confirm the analytical insights and connections in finite samples.

摘要

二次推理函数方法是相关数据分析中的一种流行方法。二次推理函数是基于多组得分方程（或扩展得分方程）制定的，这些方程过度识别了感兴趣的回归参数，并提高了相关错误指定下广义估计方程的效率。在本说明中，我们通过单独求解每组分数方程并组合这些解来提供二次推理函数的替代解。我们提供了一个见解，即从不同的分数方程组分别获得的估计量的最佳加权组合渐近等同于通过二次推理函数获得的估计量。我们进一步建立最优加权估计器的推理结果，并将这些见解扩展到具有过度识别估计方程的一般设置。进行模拟研究以确认有限样本中的分析见解和联系。