向平稳模型收缩的非参数协方差估计

IF 4.4 2区 数学 Q1 STATISTICS & PROBABILITY
T. A. Blake, Yoonkyung Lee
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引用次数: 2

摘要

非结构化协方差矩阵的估计是困难的,因为参数空间维度和估计应该满足的正定约束带来了挑战。我们使用正定矩阵的Cholesky分解来考虑纵向数据的一般非参数协方差估计框架。时间顺序测量的协方差矩阵由具有无约束项的下三角矩阵对角化,无约束项在统计上可解释为变系数自回归模型的参数。使用Cholesky分解的这种双重解释,并考虑到不规则采样时间点,我们将协方差估计视为二变量平滑,并将其放入正则化框架中,以获得协方差模型中所需的简单形式。将平稳性视为协方差中的简单性或简约性的一种形式,我们分别对具有取决于时滞及其正交方向的分量的变系数函数进行建模,并惩罚拟合函数中捕获非平稳性的分量。我们演示了使用平滑样条框架的协方差估计器的构造。模拟研究表明,与纵向数据设置中提出的替代估计相比,我们的方法具有优势。我们分析了一个纵向数据集来说明该方法的应用,并将我们的估计与替代模型的估计进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonparametric covariance estimation with shrinkage toward stationary models
Estimation of an unstructured covariance matrix is difficult because of the challenges posed by parameter space dimensionality and the positive‐definiteness constraint that estimates should satisfy. We consider a general nonparametric covariance estimation framework for longitudinal data using the Cholesky decomposition of a positive‐definite matrix. The covariance matrix of time‐ordered measurements is diagonalized by a lower triangular matrix with unconstrained entries that are statistically interpretable as parameters for a varying coefficient autoregressive model. Using this dual interpretation of the Cholesky decomposition and allowing for irregular sampling time points, we treat covariance estimation as bivariate smoothing and cast it in a regularization framework for desired forms of simplicity in covariance models. Viewing stationarity as a form of simplicity or parsimony in covariance, we model the varying coefficient function with components depending on time lag and its orthogonal direction separately and penalize the components that capture the nonstationarity in the fitted function. We demonstrate construction of a covariance estimator using the smoothing spline framework. Simulation studies establish the advantage of our approach over alternative estimators proposed in the longitudinal data setting. We analyze a longitudinal dataset to illustrate application of the methodology and compare our estimates to those resulting from alternative models.
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来源期刊
CiteScore
6.20
自引率
0.00%
发文量
31
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