title: Effective dimension reduction for sparse functional data.
abstract: We propose a method of effective dimension reduction for functional data, emphasizing the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects. The proposed method borrows strength across the entire sample and provides a way to characterize the effective dimension reduction space, via functional cumulative slicing. Our theoretical study reveals a bias-variance trade-off associated with the regularizing truncation and decaying structures of the predictor process and the effective dimension reduction space. A simulation study and an application illustrate the superior finite-sample performance of the method.
authors.affiliation: Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5S 3G3, Canada.
authors.forename: F
authors.initials: F
authors.lastname: Yao
authors.affiliation: Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5S 3G3, Canada.
authors.forename: E
authors.initials: E
authors.lastname: Lei
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A. wu@stat.ncsu.edu.
authors.forename: Y
authors.initials: Y
authors.lastname: Wu
keywords: Cumulative slicing; Effective dimension reduction; Inverse regression; Sparse functional data