CMStatistics 2016: Start Registration
View Submission - CMStatistics
B0371
Title: On the perfect reconstruction of partially observed (non-)sparse functional data Authors:  Dominik Liebl - University Bonn (Germany) [presenting]
Alois Kneip - University of Bonn (Germany)
Abstract: A new prediction procedure is proposed that allows to reconstruct functional data from their fragmental observations. Similarly to the context of sparse functional data, it is assumed that only noisy discretization points of the random functions are observable. By means of a double asymptotic, we derive the uniform rates of consistency of our functional PCA based estimator for all cases from (moderately) sparse to densely sampled discretization points per function. Furthermore, we derive verifiable a condition, under which our prediction procedure allows for a perfect reconstruction (i.e., without any prediction error) of the unobserved functional fragments. Finite sample properties are investigated through simulations. Applicability of our prediction method is demonstrated by a real data study in which we seek to reconstruct electricity price functions.