Mean and Covariance Estimation for Functional Snippets

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 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.for this article are available online.

Automated summary

This article deals with the estimation of mean and covariance functions for functional snippets. It proposes a hybrid strategy that decomposes the covariance function into a variance function component and a correlation function component. It also introduces a new estimator for the variance of measurement errors. The effectiveness of the proposed methods is demonstrated through theoretical analysis and numerical simulations.