Title: Mean and covariance estimation for functional snippets
Authors: Zhenhua Lin - University of California, Davis (United States) [presenting]
Jane-Ling Wang - University of California Davis (United States)
Abstract: The focus is on the estimation of the mean function and the covariance function of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much smaller 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 by local linear smoothing, while the correlation part is modeled parametrically to handle the missing information in the far off-diagonal regions. Both theoretical analysis and numerical simulations suggest that this divide-and-conquer strategy is effective and efficient. In addition, we propose an efficient 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.