纵向数据下均值协方差联合建模中的ARMA Cholesky因子模型

ARMA Cholesky Factor Models in Joint Mean-covariance Modeling for Longitudinal Data

在广义估计方程框架下,发展了一类灵活的回归模型来参数化协方差结构.通过合并广泛使用的修正的Cholesky分解和滑动平均Cholesky分解,得到自回归滑动平均Cholesky分解.该分解能够参数化更一般的协方差结构,且其输入具有清晰的统计解释.对这些输入建立回归模型,并利用拟Fisher迭代算法估计回归系数.均值和协方差模型中的参数估计皆具有相合性和渐近正态性.最后通过模拟研究考察了所提方法的有限样本表现.

We develop a kind of flexible regression models to parameterize the covariance structure within the framework of generalized estimating equations.Combining the frequently-used modified Cholesky decomposition and moving average Cholesky decomposition,we obtain the autoregressive moving average Cholesky decomposition which may be able to parameterize more general covariance structure.The entries in this decomposition have clear statistical interpretation.These entries are modeled by regression models and the regression coefficients are estimated via a quasi Fisher iterative algorithm.The resulting estimators for the parameters in both the mean and covariance models are consistent and asymptotically normally distributed.Simulations are conducted to illustrate the finite sample performance of the proposed approach.