Statistics Seminar
| Date/Time: | Monday, 10 Mar 2014 from 4:10 pm to 5:00 pm |
|---|---|
| Location: | Snedecor 3105 |
| Cost: | Free |
| URL: | www.stat.iastate.edu |
| Contact: | Jeanette |
| Phone: | 515-294-3440 |
| Channel: | College of Liberal Arts and Sciences |
| Categories: | Lectures |
| Actions: | Download iCal/vCal | Email Reminder |
In modern scientific experiments we often face analysis with functional data, where the observations are sampled from random process, together with a potentially large number of non-functional covariates. The complex nature of functional data makes it difficult to directly apply existing methods to model selection and estimation. We propose and study a new class of semiparametric functional linear models to characterize the regression between a scalar response and multiple covariates, including both functional and scalar types. This method provides a united and flexible framework to jointly model functional and non-functional predictors, identify important covariates, and improve efficiency and interpretability of the estimates. Featured with two types of regularization: the shrinkage on the effects of both types of covariates and the truncation on principal components of the functional predictors, the new approach treats functional predictors from a nonparametric perspective and focuses on inferring the parametric structure of the scalar covariates. The underlying process of the functional predictor is considered genuinely in finite-dimensional, and a key contribution is to associate the impact of truncation explicitly with the asymptotic behavior. We then establish consistency and oracle properties under mild conditions by allowing ultra-large number of scalar covariates and simultaneously choosing the significant functional predictors. We illustrate the performance of the proposed method with simulation studies, and then apply it to the motivating fMRI brain image data.