Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline smoother that is designed for covariance smoothing and can be used for sparse functional or longitudinal data. We propose a fast algorithm for covariance smoothing using leave-one-subject-out cross-validation. Our simulations show that the proposed method compares favorably against several commonly used methods. The method is applied to a study of child growth led by one of coauthors and to a public dataset of longitudinal CD4 counts.

中文翻译：

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稀疏函数数据的快速协方差估计。


噪声样本协方差的平滑是函数数据分析的重要组成部分。我们提出了一种基于惩罚样条和相关软件的新颖协方差平滑方法。所提出的方法是一种双变量样条平滑器，专为协方差平滑而设计，可用于稀疏函数或纵向数据。我们提出了一种使用留一主题交叉验证进行协方差平滑的快速算法。我们的模拟表明，所提出的方法优于几种常用的方法。该方法应用于由一位共同作者领导的儿童生长研究以及纵向 CD4 计数的公共数据集。