Self-Modeling for Functional Data

• Activity Number: 99
• Type: Other
• Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
• Sponsor: ASA
• Author(s): Mary J. Lindstrom*+
• Companies: University of Wisconsin, Madison

Abstract

Functional data arise when the ideal observation for each experimental unit is a curve or function. Typically, we do not observe the actual curve but instead obtain noisy observations at a number of points along the curve for each individual. A functional data set is then made up of these data curves, one or more per individual. Self-modeling is a semiparametric approach to modeling functional data which pools shape information across curves by postulating a common (usually smooth) shape or template function. Differences among individuals are accounted for by simple, individual-specific, random transformations of this common shape function. In practice, the shape function is modeled as using a flexible family of functions. Typical goals in analyzing functional data include estimating the common curve shape for the population from which the sample of individuals was drawn, describing the between- and within-curve variability structure, estimating individual curves, and testing for differences between groups of curves. This lecture will address each of these goals in the self-modeling framework.