|
|||||
|
|
A Simultaneous Confidence Band for Dense Longitudinal Regression |
|
| Authors: | Q Song R Liu L Yang |
| Institution: | 1. Department of Mathematical Sciences, The University of Texas at Dallas, Dallas, Texas, USA;2. Department of Mathematics and Statistics, The University of Toledo, Toledo, Ohio, USA;3. Center for Advanced Statistics and Econometrics Research, Soochow University, Suzhou, China;4. Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, USA |
| Abstract: | We present a method of using local linear smoothing to construct simultaneous confidence bands for the mean function of densely spaced functional data. Our approach works well under mild conditions. In addition, the local linear estimator and its accompanying confidence band enjoy semiparametric efficiency in the sense that they are asymptotically equivalent to the counterparts obtained from the random trajectories entirely observed without errors. We illustrate the performance of the proposed confidence band through a simulation study. Furthermore, an application in food science is presented. |
| Keywords: | Confidence band Functional data Karhunen-Loève L2 representation Local linear smoothing Strong approximation |