Title: On the optimal reconstruction of partially observed functional data
Authors: Alois Kneip - University of Bonn (Germany)
Dominik Liebl - University Bonn (Germany) [presenting]
Abstract: A new reconstruction operator is proposed which aims to recover the missing parts of a function given the observed parts. The new reconstruction operator belongs to a new large class of functional operators which includes the classical regression operators, considered so far, as a special case. We show the optimality of our reconstruction operator among this new class of operators. Our estimation theory allows for autocorrelated functional data and considers the practically relevant situation where each of the n functions is observed at $m$ discretization points. We derive uniform rates of consistency for our nonparametric estimation procedures using a double asymptotic that allows investigate all data scenarios from almost sparse to dense functional data. The finite sample properties are investigated through simulations and a real data application.