A Note on Generalized Functional Linear Model and Its Application

• Type of Material: Article
• Authors: Qi Long, Emory University
• Language: English
• Date: 2012-09-01
• Publisher: Elsevier
• Publication Version: Author Accepted Manuscript (After Peer Review)
• Copyright Statement: © 2012 Elsevier B.V.
• License: Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International
• Final Published Version (URL): http://dx.doi.org/10.1016/j.jspi.2012.02.027
• Title of Journal or Parent Work: Journal of Statistical Planning and Inference
• ISSN: 0378-3758
• Volume: 142
• Issue: 9
• Start Page: 2599
• End Page: 2606
• Grant/Funding Information: This work was supported in part by PHS Grant UL1 RR025008 from the Clinical and Translational Science Award program, National Institutes of Health, National Center for Research Resources.
• Keywords: Mathematics; Statistics & Probability; SMOOTHING SPLINES ESTIMATORS; Generalized functional linear model; Science & Technology; Measurement errors; Physical Sciences; Spline smoothing; REGRESSION
• Research Categories: Biology, Bioinformatics; Biology, Biostatistics

Abstract

Motivated by a biomarker study for colorectal neoplasia, we consider generalized functional linear models where the functional predictors are measured with errors at discrete design points. Assuming that the true functional predictor and the slope function are smooth, we investigate a two-step estimating procedure where both the true functional predictor and the slope function are estimated through spline smoothing. The operating characteristics of the proposed method are derived; the usefulness of the proposed method is illustrated by a simulation study as well as data analysis for the motivating colorectal neoplasia study.