title: Fast methods for spatially correlated multilevel functional data.
abstract: We propose a new methodological framework for the analysis of hierarchical functional data when the functions at the lowest level of the hierarchy are correlated. For small data sets, our methodology leads to a computational algorithm that is orders of magnitude more efficient than its closest competitor (seconds versus hours). For large data sets, our algorithm remains fast and has no current competitors. Thus, in contrast to published methods, we can now conduct routine simulations, leave-one-out analyses, and nonparametric bootstrap sampling. Our methods are inspired by and applied to data obtained from a state-of-the-art colon carcinogenesis scientific experiment. However, our models are general and will be relevant to many new data sets where the object of inference are functions or images that remain dependent even after conditioning on the subject on which they are measured. Supplementary materials are available at Biostatistics online.
authors.affiliation: Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8203, USA. staicu@stat.ncsu.edu
authors.forename: Ana-Maria
authors.initials: AM
authors.lastname: Staicu
authors.forename: Ciprian M
authors.initials: CM
authors.lastname: Crainiceanu
authors.forename: Raymond J
authors.initials: RJ
authors.lastname: Carroll
mesh_terms: D000465:Algorithms; D000704:Analysis of Variance; D000818:Animals; D001699:Biometry / Q000379:methods*; D002087:Butyrates / Q000009:adverse effects; D003110:Colonic Neoplasms / Q000139:chemically induced / Q000209:etiology / Q000378:metabolism; D003198:Computer Simulation; D050760:Cyclin-Dependent Kinase Inhibitor p27 / Q000378:metabolism; D004032:Diet / Q000009:adverse effects; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D025341:Principal Component Analysis; D012984:Software; D018709:Statistics, Nonparametric
chemical_list: D002087:Butyrates; D050760:Cyclin-Dependent Kinase Inhibitor p27