论文标题
功能片段的平均值和协方差估计
Mean and Covariance Estimation for Functional Snippets
论文作者
论文摘要
我们考虑对功能片段的平均值和协方差函数的估计，它们是在单个特定的下间情节上可能不规则地观察到的功能的简短段，比整个研究间隔短得多。功能片段的协方差函数的估计是具有挑战性的，因为完全丢失了协方差结构的远距离区域区域的信息。我们通过将协方差函数分解为方差函数组件和相关函数组件来解决这一困难。可以通过非参数有效地估计方差函数，而相关部件的参数可能具有越来越多的参数来建模，以处理遥远的外部区域区域中缺少的信息。理论分析和数值模拟都表明，这种混合策略％划分和纠纷策略是有效的。此外，我们为测量误差方差提出了一个新的估计量，并分析其渐近特性。从噪声测量值估计方差函数需要此估计器。
We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval. Estimation of the covariance function for functional snippets is challenging since information for the far off-diagonal regions of the covariance structure is completely missing. We address this difficulty by decomposing the covariance function into a variance function component and a correlation function component. The variance function can be effectively estimated nonparametrically, while the correlation part is modeled parametrically, possibly with an increasing number of parameters, to handle the missing information in the far off-diagonal regions. Both theoretical analysis and numerical simulations suggest that this hybrid strategy % divide-and-conquer strategy is effective. In addition, we propose a new estimator for the variance of measurement errors and analyze its asymptotic properties. This estimator is required for the estimation of the variance function from noisy measurements.
