A1185
Title: On optimal prediction of missing functional data with memory
Authors: Tommi Sottinen - University of Vaasa (Finland) [presenting]
Pauliina Ilmonen - Aalto University School of Science (Finland)
Nourhan Shafik - Aalto University (Finland)
Germain Van Bever - Universite de Namur (Belgium)
Lauri Viitasaari - Aalto University (Finland)
Abstract: The problem of reconstructing missing parts of functions based on their observed segments is considered. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the L2-optimal reconstruction of the missing parts. These functions are obtained as solutions of explicit integral equations. In the discrete case, approximations of the solutions provide consistent expressions of all missing values of the processes. Rates of convergence of these approximations, under extra assumptions on the transformation function, are provided. In the case of Gaussian processes with a parametric covariance structure, the estimation can be conducted separately for each function, and yields nonlinear solutions in presence of memory. Simulated examples show that the proposed reconstruction indeed fares better than the conventional interpolation methods in various situations.
