EFFICIENT ESTIMATION IN SEMIVARYING COEFFICIENT MODELS FOR LONGITUDINAL/CLUSTERED DATA
EFFICIENT ESTIMATION IN SEMIVARYING COEFFICIENT MODELS FOR LONGITUDINAL/CLUSTERED DATA
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DOI：
10.1214/15-aos1385
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发表时间：
2016-10-01
影响因子：
4.5
通讯作者：
Li, Jialiang
中科院分区：
文献类型：
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作者：
Cheng, Ming-Yen;Honda, Toshio;Li, Jialiang
在纵向/聚类数据的半变系数建模中，主要关注的通常是涉及未知常系数的参数分量。首先，我们研究了一般情况下常系数估计的半参数有效界。它可以通过使用真实的受试者内协方差矩阵的样条回归来实现，而真实的受试者内协方差矩阵在现实中通常不可用。因此，我们提出了一个估计时的协方差矩阵是未知的，只依赖于指数变量。首先，我们估计的协方差矩阵使用残差从初步估计的基础上工作的独立性和样条和局部线性回归。然后，使用协方差矩阵估计，我们再次使用样条回归来获得我们的最终估计。在正态性假设下，它达到了半参数有效界，并且即使在正态性被破坏的情况下，它也是一类估计中渐近协方差阵最小的估计。我们的理论结果保持无论是在主题内的观察分歧或当它是一致有界的。此外，就数值性能而言，使用非参数分量的局部线性估计量优于使用样条估计量的上级。通过对一个真实的数据实例的仿真和应用，将所提出的方法与工作独立估计和一些现有的方法进行了比较。
In semivarying coefficient modeling of longitudinal/clustered data, of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression using the true within-subject covariance matrices, which are often unavailable in reality. Thus, we propose an estimator when the covariance matrices are unknown and depend only on the index variable. First, we estimate the covariance matrices using residuals obtained from a preliminary estimation based on working independence and both spline and local linear regression. Then, using the covariance matrix estimates, we employ spline regression again to obtain our final estimator. It achieves the semiparametric efficiency bound under normality assumption and has the smallest asymptotic covariance matrix among a class of estimators even when normality is violated. Our theoretical results hold either when the number of within-subject observations diverges or when it is uniformly bounded. In addition, using the local linear estimator of the nonparametric component is superior to using the spline estimator in terms of numerical performance. The proposed method is compared with the working independence estimator and some existing method via simulations and application to a real data example.