Estimating a smooth covariance for functional data
提出两种在有测量误差时估计平滑协方差函数的方法，分别基于低秩近似和Cholesky分解，通过罚回归实现平滑，并用奶牛产奶量和果蝇产卵模式数据验证。
Functional data analysis frequently involves estimating a smooth covariance function based on observed data. This estimation is essential for understanding interactions among functions and constitutes a fundamental aspect of numerous advanced methodologies, including functional principal component analysis. Two approaches for estimating smooth covariance functions in the presence of measurement errors are introduced. The first method employs a low-rank approximation of the covariance matrix, while the second ensures positive definiteness via a Cholesky decomposition. Both approaches employ the use of penalized regression to produce smooth covariance estimates and have been validated through comprehensive simulation studies. The practical application of these methods is demonstrated through the examination of average weekly milk yields in dairy cows as well as egg-laying patterns of Mediterranean fruit flies.