Nonparametric estimation of large covariance matrices of longitudinal data
Nonparametric estimation of large covariance matrices of longitudinal data
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DOI：
10.1093/biomet/90.4.831
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发表时间：
2003-12-01
期刊：
影响因子：
2.7
通讯作者：
Pourahmadi, M
中科院分区：
文献类型：
--
作者：
Wu, WB;Pourahmadi, M
由于非结构化协方差矩阵的正定性限制，估计是很困难的。这个障碍是通过将每个变量回归到它的前身来消除的，因此协方差矩阵的估计被证明等同于估计一系列变系数和变阶回归模型。我们的框架类似于使用升阶自回归模型来逼近平稳时间序列的协方差矩阵或谱。作为说明，我们采用Fan&Zhang(2000)的泛函线性模型的两步估计，提出了协方差阵的非参数估计，并保证其正定。简而言之，使用像AIC和BIC这样的惩罚似然准则，为(自动)回归模型的序列找到了合适的顺序。建立了协方差矩阵分量的局部多项式估计的一些渐近结果。分析了两个纵向数据集，以说明该方法。仿真研究表明，当协方差矩阵较大时，非参数协方差估计比样本协方差估计具有更大的优势。
Estimation of an unstructured covariance matrix is difficult because of its positive-definiteness constraint. This obstacle is removed by regressing each variable on its predecessors, so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying-coefficient and varying-order regression models. Our framework is similar to the use of increasing-order autoregressive models in approximating the covariance matrix or the spectrum of a stationary time series. As an illustration, we adopt Fan & Zhang's (2000) two-step estimation of functional linear models and propose nonparametric estimators of covariance matrices which are guaranteed to be positive definite. For parsimony a suitable order for the sequence of (auto) regression models is found using penalised likelihood criteria like AIC and BIC. Some asymptotic results for the local polynomial estimators of components of a covariance matrix are established. Two longitudinal datasets are analysed to illustrate the methodology. A simulation study reveals the advantage of the nonparametric covariance estimator over the sample covariance matrix for large covariance matrices.